Lord Downpatrick (Kent line). The Prince of Thurn und Taxis is still single (gulp). Prince Constantine of Greece is pretty hunky. Alas, with the rise reporting on the celebrity and not on the aristocracy, I can't think of many. You might look at Netty's page. She used to have a listing, updated regularly.
I'm sure he was-in the 1960s until he became King Constantine and married Anne-Marie of Denmark. Are you sure you're not thinking of Prince Philippos of Greece, Constantine's youngest son? He's not too hard on the eye; sadly, I think he has a girlfriend, so he may not be on the market, so to speak.
Edited to add:
Or do you mean MC's eldest son? I always forget he's Prince Constantine, and I tend to think of the king when I hear that name.
If you're looking for a Catholic royal:
Archduke Alexander de Habsbourg-Lorraine is single. Alexander is less inbred-looking than his older brother Imre. However, if you're not his cousin, he may not be interested. Not sure. His sister Gabby prefers to only date cousins, as did his parents, so he may also be unavailable to you (unless you're related to him).
Sebastian of Luxembourg is single. So is his cousin Josef of Lichtenstein. The oldest son of the Duke of Braganza is single and an adult; so is the Brazilian heir.
If you prefer ladies, then there's always Alexandra of Luxembourg, Annunciata and Astrid of Liechtenstein, Archduchess Priscilla, Maria-Laura of Belgium and Laetitia of Belgium.