Wasn't the Klingon Bird of Prey originally designed for Star Trek III when the main baddies were supposed to *Romulan* - hence the very Romulan design and color - and *name*, as up 'till that point, only the Romulans had ships named "Bird of Prey", that were painted like birds.
So in my personal head cannon, at least the original "Klingon" Birds of Prey were a Romulan design that was traded to the Klingons for the Klingon D-7 and later style ships that we saw the Romulans using in TOS and on the Kobyashi Maru simulation in Star Trek II...
Of course...I guess that doesn't make sense considering that in Enterprise we saw a 22nd century Klingon proto-Bird of Prey. (Unless the Klingins and Romulans were trading designs even back then.)
Makes me wonder what happened sometimes in the 23rd century to make the Klingons and Romulans go from tenative allies to species who hate each other so much...? Though maybe the Bird(s) of Prey and D-7's were *captured* ships used by both species...?