Is there a generally accepted term for "Christians in Communion with the Bishop of Rome"?

Perhaps a bit of history concerning the label "Roman Catholic" will serve us well by shedding light upon (if not answering) this very good question.

The term "Roman Catholic" appears to be directly connected to the Reformation in England, and was originally an imposed derogatory term of condescension.

The Catholic Encyclopedia references the Oxford English Dictionary:

In the "Oxford English Dictionary", the highest existing authority upon questions of English philology, the following explanation is given under the heading "Roman Catholic".

The use of this composite term in place of the simple Roman, Romanist, or Romish; which had acquired an invidious sense, appears to have arisen in the early years of the seventeenth century. For conciliatory reasons it was employed in the negotiations connected with the Spanish Match (1618-1624) and appears in formal documents relating to this printed by Rushworth (I, 85-89). After that date it was generally adopted as a non-controversial term and has long been the recognized legal and official designation, though in ordinary use Catholic alone is very frequently employed. (New Oxford Dict., VIII, 766)

One of the earliest appearances of the term "Roman Catholic" is in a book written by Robert Crowley called "A Deliberat Answere", printed in 1588. Though preferring to use the terms "Romish Catholike" or "Popish Catholike", he also writes of those "who wander with the Romane Catholiques in the uncertayne hypathes of Popish devises" (p. 86). A study of these and other early examples in their context shows plainly enough that the qualification "Romish Catholic" or "Roman Catholic" was introduced by Protestant divines who highly resented the Roman claim to any monopoly of the term Catholic. In Germany, Luther had omitted the word Catholic from the Creed, but this was not the case in England.

It is noteworthy that by the 17th century the label of "Roman Catholic," although a term of condescension, began to be subordinately accepted by both the Catholic clergy, as well as the laity, most prevalantly in heavily persecuted Ireland.

...[T]he use of the term Roman Catholic continued to be a mark of condescension, and language of much more uncomplimentary character was usually preferred. It was perhaps to encourage a friendlier attitude in the authorities that Catholics themselves henceforth began to adopt the qualified term in all official relations with the government. Thus the "Humble Remonstrance, Acknowledgment, Protestation and Petition of the Roman Catholic Clergy of Ireland" in 1661, began "We, your Majesty's faithful subjects the Roman Catholick clergy of Ireland".

Up until the turn of the 20th century, Catholic clergy were "strongly advised" to maintain the official title of "Roman Catholic" for the sake of separation from the Church of England.

In 1897 at the Diamond Jubilee of the accession of Queen Victoria, and again in 1901 when Edward VII succeeded to the throne, the Catholic episcopate desired to present addresses, but on each occasion it was intimated to the cardinal that the only permissible style would be "the Roman Catholic Archbishop and Bishops in England". Even the form "the Cardinal Archbishop and Bishops of the Catholic and Roman Church in England" was not approved. On the first occasion no address was presented, but in 1901 the requirements of the Home Secretary as to the use of the name "Roman Catholics" were complied with, though the cardinal reserved to himself the right of explaining subsequently on some public occasion the sense in which he used the words (see Snead-Cox, "Life of Cardinal Vaughan", II, 231-41). Accordingly, at the Newcastle Conference of the Catholic Truth Society (Aug., 1901) the cardinal explained clearly to his audience that "the term Roman Catholic has two meanings; a meaning that we repudiate and a meaning that we accept." The repudiated sense was that dear to many Protestants, according to which the term Catholic was a genus which resolved itself into the species Roman Catholic, Anglo-Catholic, Greek Catholic, etc. But, as the cardinal insisted, "with us the prefix Roman is not restrictive to a species, or a section, but simply declaratory of Catholic." The prefix in this sense draws attention to the unity of the Church, and "insists that the central point of Catholicity is Roman, the Roman See of St. Peter."

All things considered, I believe its safe to say that all English speaking countries refer to Christians in union with the Pope (both Eastern and Western) as "Roman Catholics" mainly because of the trickled down term that has been imposed on papal subordinates by the British Crown.

Of course there are many other reasons...

Long story short - the Reformation complicated things terminologically for English speaking Christians, as with many other aspects within Christianity.

It is noteworthy that the representative Anglican divine, Bishop Andrewes, in his "Tortura Torti" (1609) ridicules the phrase Ecclesia Catholica Romana as a contradiction in terms. "What," he asks, "is the object of adding 'Roman'? The only purpose that such an adjunct can serve is to distinguish your Catholic Church from another Catholic Church which is not Roman"

I would like to reiterate that, although this may not answer your question satisfactorily, it may at least shed some light...

Personal experience/opinion...

I wish the label of Roman Catholic would be done away with altogether. I remember the first time I encountered this term. I was going through confirmation (around the mid '90s) and had only been taught by friends, family, and fellow parishioners that we were all simply "Catholics." I attended a youth retreat with thousands of other teenagers. I noticed someone wearing a shirt that said "Proud to be a Roman Catholic." I asked my youth leader, "What is a Roman Catholic?" He responded, "Well I guess it is just an emphasis on the fact that the Pope is our Pope and he happens to be the Bishops of Rome. Maybe that shirt is to signify to Protestants that he is marked by the Anti-Christ." (He was joking of course)

The label is self contradictory. If what we say is true...that the Church is all inclusive...then we shouldn't confuse people by clinging to an archaic label that was forced upon us in the first place. Perhaps "Petrine Catholics" or something of that nature would be more fitting. This question should not exist.

Maybe we should all write a letter to his Holiness suggesting a better label for the world to recognize.