Back many years ago, perhaps 1950's, 60's or 70's, the word "bird" was used to describe a woman, and more typically a girlfriend, as in the phrase "She's a top bird"
Was there a male equivalent to this word?
Bird as a term was applied to women in Middle English. The slang usage was revived in the 20th century as (often disparaging) slang. (The Oxford English Dictionary explains:
d. A maiden, a girl. [In this sense bird was confused with burde , burd n., originally a distinct word, perhaps also with bryd(e bride n.1; but later writers understand it as figurative sense of 1 or 2.] In modern (revived) use: a girl, woman (often used familiarly or disparagingly) (slang).
There often aren't cross-gender equivalents of terms. For one, the sexes were often not thought of in the same way. Sexual looseness for women was often scandalous; for men it was sometimes celebrated. For another, the roles people played were different. Courtship, family structures, and employment were often highly gendered. So with a very general term like bird, the best I can find is another animal-like word that would refer to a man during the same time period you describe.
2a. GUY // "some young … cat asked me to go drinking with him" — Jack Kerouac
Kerouac writing it places the usage firmly in the 1950s beat culture. It's also associated with jazz. While other terms (bloke, dude, guy) would be contemporaneous, the animal terms make the two feel more similar.
Lover-boy is often deployed in a similar vein, and was around in the '50s and '60s.
Mrs. Higgins popped another chocolate in her mouth, sucked on it noisily, then drawled, "It's a nice idea, lover boy, but let's face it— you just ain't got the guts. And since you haven't, there's nothing you can do but what I tell you, when I tell you, the way I tell you. You're mine ...
Theodore R Cogswel, Lover Boy. 1954