Have Creationists advanced any particular Theories of Origin that they claim are falsifiable via the scientific method?

The problem with this question is a false assumption: That Creationists would generally strive to create a model that is falsifiable.

Rather, Creationists, especially the Young-Earth variety, would contend that no origin theory is falsifiable, merely because we cannot experiment on what has already past. Creationists have developed their own distinction of two types of science to explain their thoughts.

The two types of science are:

1. Observational Science
2. Historical Science

Observational science is based off of observable, testable, repeatable, and falsifiable events. Essentially, this is what everyone else just calls science.

Historical science is, according to Answers in Genesis (the rapidly becoming "official" YEC source), "[the process of] interpreting evidence from past events based on a presupposed philosophical point of view." In essence, they are completely different things and perhaps historical science should not be called science at all.

The point nearly every Creationist strives to make is that The Theory of Evolution (distinct from the observational science of biological evolution) is a religion just as much as Creationism, and depending on your "presupposed philosophical point of view" you will reach different conclusions about the origins of the Universe. They contend that the YEC perspective looks at exactly the same evidence as The ToE, both accepting the observed sciences as valid, yet they reach different conclusions about origins. They are both theories of historical science.

So some this up, another article on AiG explains:

A creationist astronomer sees comets in the universe and realizes they have a limited “existence” of at most 100,000 years. He concludes that the universe must be less than 100,000 years old. A cosmic evolutionary astronomer sees the same thing but concludes there must be a constant source of comets, because he believes the universe is 13.7 billion years old. He would, of course, claim that he arrived at that date due to observational measurements of light from distant galaxies. The creationist astronomer would then hypothesize an explanation for the distant starlight problem, which the evolutionist would rebut, etc.

That same source article also attempts to explain the difference and legitimize the distinction between observational science and historical science.

• Another source that discusses "two types of science" on AiG.

A fundamental tenet of Christian belief is that God created the world, with the primary evidence for this found in the Book of Genesis. What is usually meant by Creationism is not so much about whether this is read literally or symbolically, but about creating a "science" that can be put alongside the science of evolution and therefore defend the biblical account.

'Young Earth Creationism'

Traditional creationism, often known as ‘Young-earth Creationism’ holds that the world was created in just six days, and only a few thousand years ago. Many Young-earth Creationists do not insist on the earth having been created barely six thousand years ago, but they feel certain it was created within the last ten thousand years. Of course, this means that much of what is taught in science is to be regarded as wrong.

One of the most implausible scientific hypotheses of Young Earth Creationists is that the half-lives of radioactive elements altered dramatically and permanently as a result of the biblical Flood, thus leading to false scientific estimates of the age of the earth. The limitation here is that this can only ever be a hypothesis and can not be used experimentally to falsify the accepted age of the earth. As it happens, this has been falsified by the evidence that extra-terrestrial elements have exactly the same half-lives as do terrestrial elements, but there is no evidence that the YEC proponents anticipated this or claimed their hypothesis to be falsifiable.

'Old Earth Creationism'

Old-earth Creationists accept that science has proven its case, that the world is over four billion years old. They seek to harmonise this with the Bible by looking for innovative ways of interpreting the Book of Genesis, to allow both science and the Bible to be seen as true. In other words, there is no overt sense of demonstrating the age of the earth or the evolution of species to be falsifiable, as long as God guided the process. What is regarded as falsifiable is that evolution progressed by natural selection.

Unusual among Creationists is Michael J. Behe, because he is a scientist and actually understands scientific method and has proposed a scientifically falsifiable thesis of biological origins. Behe believes that complexity in the structure of the biochemical system can not be explained by evolution. He evokes images of immensely complex biochemical systems, claiming that the complexity of these systems is irreducible and therefore could not be the result of an evolutionary process, pointing to intelligent design. Among his examples are the mechanisms of blood clotting, the cilium mechanism used by bacteria to move around, and the human eye. This is a falsifiable thesis because if these mechanisms are not irreducibly complex, with no simpler mechanisms from which they could have evolved, then his thesis of irreducible complexity is falsified. In fact, each of these examples has been examined by critics and examples from which evolution by natural selection could have occurred have been found by the scientific method.

'Theological Creationism'

Somewhat similar to Old Earth Creationism is 'theological evolution'. Because it adopts the scientific consensus, with a theologiccal component, this theory of origin is not scientifically falsifiable, except to the extent that a major body of science is falsifiable. Pope Francis, in a speech given at a Pontifical Academy of Sciences, stated:

“[God] created beings and allowed them to develop according to the internal laws that he gave to each one, so that they were able to develop and to arrive and their fullness of being. He gave autonomy to the beings of the universe at the same time at which he assured them of his continuous presence, giving being to every reality. And so creation continued for centuries and centuries, millennia and millennia, until it became which we know today, precisely because God is not a demiurge or a magician, but the creator who gives being to all things... The Big Bang, which nowadays is posited as the origin of the world, does not contradict the divine act of creating, but rather requires it. The evolution of nature does not contrast with the notion of creation, as evolution presupposes the creation of beings that evolve."

Just glimpsing at the question, there are inherent falsifiable things in "creationism".

I am going to use a Hypothesis / Falsifiable argument format

• H: Life comes from life

• F: If a non-living (rock) thing becomes alive

• H: Living animals cannot change their kind through reproduction

• F: If a cat breeds with another cat, and produces a non-cat (like a pig)

Side note: there are disparity between creationists about what the bible teaches if plants (created day 3), are alive or not alive

I am sure you can find more if you look for them, but the bible is a relatively short book with only a few chapters dedicated to the creation story; these 2 points are what I assume to be the root of all creationism.

Creationists do sometimes make falsifiable theories and predictions, but I want to note first that:

• These predictions are not universally held among all creationists, or depending on the theory even relatively common
• They are based on assumptions that are not derived from scripture and which are not even logically required by the idea of creationism or even young earth creationism. For example, as someone who believes in substantial apparent age, I could reject every such assumption. If their theories end up being falsified this should not be seen as a blow to creationism itself as they were never really part of it to begin with. As a whole creationism isn't falsifiable.

The magnetic fields of planets

D. Russell Humphreys, a YEC physicist, has produced models for the magnetic fields of each of the planets on the assumption that they are only about 6000 years old. His first predictions were produced after Jupiter and Saturn were visited but before Uranus and Neptune. His models were based on the belief that the fields were decaying from an initial strength they were created with, rather than being sustained through some process as those who believe in an old solar system argue. I don't understand the details (nor do I care enough to look into it more), but creationists still state that his models were vindicated when Voyager 2 did visit the planets.

More recently he has stated that his models are being confirmed for Mercury.

Chance and information

Creationists believe that information can only be produced from intelligences, and that all evidence so far only shows that chance reduces information. If laboratory conditions could show self-replicating structures (rather than merely amino acids) arising from a pre-biotic soup, or if they could show new function arising from mutations in nature, then this belief, which is really the whole foundation of the anti-evolution movement, would collapse.

The tricky thing is that it's very hard to characterise the results of single mutations. Switching on or off genes is one thing, but that is not considered to be an increase in information. Still, if it were possible, we would expect to eventually have clear proof of mutations producing new functions.

Dark matter/energy

The standard Big Bang model requires the existence of Dark Matter and Energy to fit our observations of the universe into the model. This Dark stuff has not been directly detected, and would be very hard to detect. Some creationists who reject the Big Bang have argued that there is no Dark stuff. But if it were to be definitively detected, that would count as a strike against them.

Reasons to Believe is an organization which presents arguments in favor of Old Earth Creation, and on their Who We Are page, founder Hugh Ross states:

One of the approaches I've developed, with the help of my RTB colleagues, is a biblical creation model that is testable, falsifiable, and predictive.

Their web site offers an overview of their "falsifiable" creation model approach, which includes:

Using a model approach supplies researchers with enough detail to assist in further study. It offers explanations for how, when, where, and why the phenomena (or system) occurs. It anticipates, or “predicts,” discoveries that could either verify or falsify the model's explanation(s). The best models also yield specific suggestions for how near-future research may help improve understanding of the systems or phenomena they attempt to explain.

One example (the first I found) of a theory which they claim is falsifiable can be found in this article:

These morphologically indistinguishable, yet genetically distinct ecomorphs can be properly considered as one of the many fingerprints that the Creator has left on His creation. In fact, if a single Creator was responsible for life, one could anticipate seeing repeated examples of the same blueprint throughout the biological realm. One would expect that a single Creator would reuse successful designs over and over again.

Note that this is not an academic article, so it's targeted at lay people, and as such the terminology is rather imprecise for my taste. It also seems to me that their claims of falsifiability are somewhat subjective, so I simply present them here as evidence that Creationists do, indeed, claim to produce falsifiable theories.