Are there any denominations that accept the gap theory?

It's a very interesting question, BYE.
I have been an insider in about 9-12 different denominations - my dad was in construction and we moved a lot.
I can say that Ray Butterworth had some points, but he actually missed/ didn't explain the background behind the gap theory.

It's really not about the darkness- because Evangelical Churches and very traditional conservative churches believe/teach in a literal 7 day creation, and scripture is very clear that in each day of Creation, there was evening and morning - the first day. There was evening and morning, the second day, etc. This is easily explained when we understand that God himself is light, and scripture also clearly says that in heaven, we have no need of the sun, for God himself is the light.
The reason that the sun was not created until the 4th day, is that God did not want people to worship the sun as the source of life.
Jews count days starting at sunset so this example of Evening and morning was the third day is totally consistent with Jewish thought.
Now the background about the "so called Gap theory". The reason it's referred to as the Gap theory is that they speculate that there must have been an indefinite gap of time between Genesis 1:1 and Genesis 1:2. The reason for this alleged gap is that the text says that the earth was without form and void, and darkness was over the face of the deep. The word "was" in vs 2 is best translated as "became". So they say that the original creation would not have been dark and formless - and this is not consistent with God's character - so they make a huge jump to speculate that the earth "became" without form and void, over millions of years. They further speculate that this Gap and the destruction occurred when the angels were cast out of Heaven, and before anything on earth was created. There are more holes in this than Swiss Cheese.
Having said that - the issue here is really about believing a young earth creation or ancient earth creation.
It's very much a secondary or tertiary position - not one of the core tenets of Faith, and so it's not considered important enough to to be included in the statement of faith of most churches.
I was a member of Evangelical Free Church of America and they major on the majors and have multiple issues that they consider non-essentials. There is even a whole book on the non-essentials, which includes issues like alcohol, mode of baptism, and some end-times views. This is one of those non-essential issues. For other, very conservative Evangelical churches, it won't be listed in the statement of faith, but would fall under the literal interpretation of Genesis as literal History - in other words - Genesis is not poetry, or symbolism, and thus their members are expected to hold the creation account as literal 7 day periods.
You would also find people who believe the Gap theory in Reformed/ Presbyterian churches, because they also often don't accept/teach Genesis as historical, and also they often discount prophecy as being symbolic, so it's very common to find Reformed people who don't believe in the 7 year tribulation and many end times issues, in Daniel and Revelation. The Presbyterian Church of America doesnt mention this in their doctrinal statement, because it's such a side issue, but I had a pastor who was 5 Point Calvinist who believed and taught the Gap theory.

There are quite a few denominations that believe that the literal 7 days of creation occurred only a few thousand years ago, while also believeing that the universe itself was created billions of years earlier.

Many of them have "Church of God" in their names, such as:

• United Church of God,
• Living Church of God,
• Restored Church of God,
• Philadelphia Church of God,
• Church of God, International,

They publish various videos and booklets, such as:

• Why Creationists Are Wrong,
• Where Do the Dinosaurs Fit?.

Advocates of the gap theory have based much of their argument on verses 1 and 2 of Genesis, because there was no light.

Do you have a reference to this argument about light? I've never heard it before.

The usual description of the gap theory is that there is an unspecified amount of time between Genesis 1:1 and 1:2. God created the universe billions of years ago (1:1), Lucifer was put in charge of the Earth and then later rebelled against God. This resulted in the destruction of much of the Earth, including its plants and animals (e.g. dinosaurs). Genesis 1:2 resumes the history with the creation week, God restoring the Earth and repopulating it.

I wrote an essay for a religion/science course twenty years ago. Genesis 1: No Need For Metaphor Here's an excerpt from it:

... In the beginning God created the heavens and the earth

The word "heavens" is sometimes translated as the singular "heaven", but the original Hebrew word is "shamayim", and like "elohim", it too is a plural word. Depending upon context, there are three meanings to this word. The first heaven is simply the earth's air, the second is space beyond the atmosphere, and the third is the location of God's throne (2Corinthians 12:2 "up to the third heaven").

Before the physical creation, there were already created spirit beings known as Angels, and symbolically referred to as stars in Job 38:4,7 and elsewhere:

"Where were you when I laid the foundations of the earth? […]
 When the morning stars [(Lucifer?'s) Angels] sang together
 And all the sons of God [(the other) Angels] shouted for joy?"

Note that "sons of" is not meant literally (as a reference to Christ would be) but a Hebrew idiom indicating "those characterized by", as in "sons of disobedience".

These angels were lead by three archangels, Gabriel, Lucifer, and Michael.

3. Genesis 1:2 "The earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters."

The earth was Notice that even though the word "was" frequently appears in italics, to indicate that it was supplied by the translators, the first use in this verse isn't italicized since there is a Hebrew word from which it has been directly translated. In Hebrew, if a simple state of being is intended, the verb "to be" is omitted. But in this case, the word doesn't indicate a state of being, as it does in English, but also a change of state. The New International Version has a footnote indicating that it could have been translated as "became", and the same Hebrew word is used in Genesis 19:26: "[…] became a pillar of salt".

The earth was without form, and void Many translations use "without form" and "void" or other similar expressions, but the translators may have been influenced by the Greek belief that the universe originated from chaos. The same Hebrew word for "void", "bohu", is translated in Isaiah 34:11 as "emptiness" in reference to a land that has been destroyed, while the word for "without form", "tohu", is translated in other verses, such as Deuteronomy 32:10, Job 12:24, Psalms 107:40, and Isaiah 24:10, and 41:29 as "ruin", "waste", "desert", "empty place", "confusion", and "wilderness". The Contemporary English Version renders this verse as:

"The earth was barren, with no form of life;"

More significantly, Isaiah 45:18 uses the same word "tohu":

"For thus says the LORD,
Who created the heavens […],
Who formed the earth and made it […],
Who did not create it in vain [tohu] […]"

providing further indication that this is not how God originally created the world, but how it later became. The RSV has "did not create it a chaos", while the NASB has "did not create it a waste place".

The earth was without form, and void; and darkness was on the face of the deep. Between verses 1 and 2 is a long period of time during which the earth must have teemed with life, as evidenced by the fossils of dinosaurs and other extinct creatures. But what was it that turned God's creation from perfection to darkness and desolation?

One thing God cannot create is character. Free will is something shared by both angels and man, who must freely choose to do God's will. Lucifer, and a third of the angels (Revelation 12:4), chose to rebel against God (Revelation 12:7-9):

"And war broke out in heaven: Michael and his angels fought with the dragon; and the dragon and his angels fought, but they did not prevail, nor was a place found for them in heaven any longer. So the great dragon was cast out, that serpent of old, called the Devil and Satan, who deceives the whole world; he was cast to the earth, and his angels were cast out with him."

It was the ensuing conflict and Lucifer's ejection from heaven that caused such massive damage to the earth.

Isaiah 14:12 refers to these events while comparing the king of Babylon to Lucifer:

"How you are fallen from heaven,
O Lucifer, son of the morning!
*How* you are cut down to the ground,
You who weakened the nations!
For you have said in your heart:
I will ascend into heaven,
I will exalt my throne above the stars of God;
I will sit on the mount of the congregation
On the farthest sides of the north;
I will ascend above the heights of the clouds,
I will be like the Most High."

and Ezekiel 28:12-15 compares (perhaps sorrowfully) the king of Tyre:

"[…] You were the seal of perfection,
Full of wisdom and perfect in beauty.
You were in Eden, the garden of God; […]
You were the anointed cherub who covers; […]
You were perfect in your ways from the day you were created,
Till iniquity was found in you."

Jesus referred to this in Luke 10:18:

"I saw Satan fall like lightening from heaven"

Peter in 2Peter 2:4:

"[…] God did not spare the angels who sinned,
but cast *them* down to [Tartarus]
and delivered *them* into chains of darkness […]"

and Jude in Jude 6:

"And the angels who did not keep their proper domain,
but left their own abode,
He has reserved in everlasting chains under darkness
for the judgement of the great day;"

But even though rejected by God, Satan still remains in charge of the earth. John 12:31, John 14:30, John 16:11, 2Corinthians 4:4, Ephesians 2:2 refer to him as "the ruler of this world", "the god of this age", etc. And in Luke 4:5-6 Satan claimed to have authority over all nations:

"Then the devil, taking Him up on a high mountain,
showed him all the kingdoms of the world in a moment of time.
And the devil said to Him, 'All this authority I will give to You,
and their glory; for *this* has been delivered to me,
and I give it to whomever I wish.'"

Jesus's non-denial of Satan's claim confirms that Satan does hold such power.

4. Genesis 1:3-5

"Then God said, 'Let there be light'; and there was light.
And God saw the light, that it *was* good;
and God divided the light from the darkness.
God called the light Day, and the darkness He called Night.
So the evening and the morning were the first day."

Even though perfect character cannot be created, God can create beings capable of using their free will to develop such character in themselves. But unlike the angels, man would be a physical being, mortal instead of immortal, and subject to permanent termination should he choose to go against God's will. As Ezekiel 18:20 says "The soul who sins shall die […]".

But first God had to clean up the nuclear winter mess that the earth had been turned into. On this first day he allowed sunlight to once again begin warming up the earth.