Tamar is still only 30 and Georgian ruling family women were famous for their beauty. I say go for it Freddy!
Oh, you probably meant one of the Trebizond Komnenai marrying her, didn't you?
Fred is a bit old for the queen.

Also he's an icky Catholic, better to go for a descendant of the great Alexios and dispose of the flaccid Angeloi usurpers.
Find a list of Byzantine generals. That'd be useful.
Indeed, but that is easier said than done... not exactly something
Wikipedia has.

**begins searching generals in list**
ETA: Well, not sure how old he was at the time, but
John Komnenos the Fat seems like a good candidate; as he was behind an unsuccessful coup in 1201...
Maybe he could marry
Tamar the Great? Though I'm not sure if she'd go through with it- Komnenos or not he's basically just a courtier (a la CK2's claimants in court). Doesn't mean she wouldn't go for it, and I definitely could see a marriage post-coup to shore up support. How this would be received in their respective courts is another matter entirely... that and I don't think the Georgians would be happy with a Castille style dynastic union vis a vis the Greeks, they're culturally and religiously close yes but not nearly THAT close... then again considering the Polish-Lithuanian Union...
The grandsons of Andronicus I are too young as of the 1190s (the Trebizond Komennoi to be), if memory serves.
Finding other male Komnenoi might be easier said than done.
Wasn't the ruler of Cyprus (well, until he crossed Richard the Lionheart) a member of the dynasty?