What case could one make for regarding King Charles Stuart as a Beatus? Just suppose one wanted to, and just suppose an enthusiastic advocate really tried to do his best? (If the very thought of this makes you go hot under the collar, please do not read any further.)
We must start with basics.
When was Beatification invented? In a funny sort of way, Beatification came before Canonisation. This is true philologically: any who indulge in Latin liturgy will be aware that by far the commonest word in liturgical Latin for a saint is beatus, whether in the Canon or the Collects. It is also true juridically; because the essence of Beatification is: the raising of a particular person to the Altars of a particular, local Church ... not of the Universal Church. And, except for certain 'Biblical' Saints, every 'saint' began with a local cultus. Only later did he or she, perhaps, become a popular saint throughout the whole Christian world; a process which might grow naturally out of pilgrimage or the distribution of relics. It is the notion of a Universal Saint which was secondary and which gradually developed. And the declaration that someone fell into that Universal category was a natural function of a Universal Primate. You would not expect the Bishop of Lesbos to have the right to dictate to the Bishop of Lincoln who was to be honoured on the calendar of his Church. So whenever a local Church wished to enhance supranationally the status of one of its own great sons or daughters, it obtained a Bull of Canonisation from the Holy See. The first known example seems to be from 993; and the system was in full flood a couple of centuries later when, for example, Ss Edward the Confessor, Richard, and Thomas Becket were so honoured by Roman Pontiffs. These instincts contributed to a process of Roman centralisation.
But local initiative did survive the Middle Ages. According to that great and erudite Pontiff, Benedict XIV, the last known local act of locally raising a man to the Altars of his local Church was a Beatification of Boniface of Lausanne by the Archbishop of Malines in 1603 (the privileges and prestige of the great local Western Primacies took a long time to fall into abeyance). And one of the first actions of Benedict XVI was to send beatifications back to the local Churches. The preliminary processes, of course, do continue to take place under the authority of the Vatican, but the significance of the act as inherently local has been reinstated. ('Benedict' seems a papal name linked with erudition and a broad understanding that 'Tradition' means something wider than 'What we've done for the last last ninety years'!)
And what actually happened at beatification was nothing like the razzamatazz (etymology??) of the modern event. What occurred was simply that Mass and Office were authorised for use, with a clear indication of limitations. Thus S Philip Neri was beatified in 1615 simply by the granting of permission for Mass and Office to be celebrated in the Oratorian Chiesa Nuova in Rome. Pope Paul V made it clear that the privilege exended to nowhere else at all, and reminded the Roman Oratorians to celebrate Philip in a comparatively low-key way.
Charles Stuart was executed in 1649. In 1662, in the Anglican Provinces of Canterbury and York, Mass and Office were promulgated by both Church and State, and were universally used within the jurisdiction of the King of England and Ireland. So ... ... could it be argued that a cultus of Blessed Charles Stuart King and Martyr is lawful, as being completely in accordance with precedent?
(Incidentally and in passing: nobody in England claimed any authority to insist that Charles Stuart be given a cultus in Poland, Peru, or the Peloponnese. And indeed, in the forms of service which were brought into use, Charles is not, as far as I have noticed, ever called 'Saint'; while the B-word is used quite generously. Referring to him as "St" seems therefore to me to lack justification. We can only be discussing the possibility of his equipollent Beatification.)
Of course, I know the objection which will be made: that Stuart was a schismatic or worse; that the ecclesial community in which his cultus flourished was schismatic or worse; hence it possessed no canonical authority or ecclesial authenticity; and so none of all this stuff 'counts'. Waste of my time.
Believe me, I can see the force of this.
Still ... one problem which this objection will have to counter is that beatifications and canonisations done by antipopes have sometimes 'stuck'. "Paschal III" canonised someone called Charlemagne, and his cultus has still not disappeared. And those canonised have included holy people who, in the Great Schism of the West, adhered to a prelate now regarded as an antipope. Yes; I know they wanted to adhere to the true pope ... perhaps wanted to do so quite desperately ... but, de facto, canonically, historically, they just didn't.
But the biggest problem which such potential critics will have to face is this.
FACT: Some of the Byzantine Churches ('Uniates') now in full peace and communion with the See of S Peter use Calendars containing Byzantine worthies who died while Rome and Byzantium were disunited; and, moreover, whose canonisations were enacted by "schismatic Greek Orthodox" synods. I have in mind the Melkite Patriarchate of Antioch (His Beatitude is a Successor of S Peter! Surely, the most senior prelate in the Catholic Church after the Pope?). (The same, I have been told, is true of the Ukrainian Church: accurate information?).
So: people who died in schism and who were then canonised by people in schism can have the cultus of a Saint within the Catholic Church.
To help to focus the minds of readers, I say now that I will decline to enable comments which criticise the thesis I have deployed WITHOUT taking seriously the sections above in red.
I add that I can myself think of a detail in Benedict XIV's historical exposition of Beatification which might undercut one part of this thesis; and of elements in the ecclesiology of Benedict XVI which could be used to subvert another. Readers may well be able to detect other flies in my ointment. Fair enough. I am privileged to have some extremely able and acute readers. But I am not going to give space to mere angry rants.