The possibilities are nigh endless... you could have one of stronger Bulgarian Tsars either take Constantinople some time in the IXth or Xth century, or, more likely, stake a claim on the throne through, say, a marriage of his son to a Byzantine princess - if there is a dynastic change in Byzantium, or a weak Emperor with dubious claim to the throne, the "Bulgarian Candidate" may become a viable contender for the throne. This basically works any time there is an independent and powerful Bulgaria, and Byzantium - so it could be as late as XIVth century, if needed.
Another possibility is a Bulgarian-descended dynasty that, however, existed within the Byzantine system (i.e. the Cometopouli manage to alter their ambitions towards the Byzantine throne). In this case, Bulgarian dynasty would be simply the same as the various ethnic Armenians that ruled the Empire from time to time. The best time for that, if you ask me, is anywhere between 1000 AD and 1180 AD or so.