What is the male equivalent of the 1960's slang "bird", meaning a woman
Solution 1:
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.
Cat. Merriam-Webster:
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.
Solution 2:
I am not sure that bird is out of use or really that derogatory. A bird is an attractive younger woman, a top bird is someone very attractive indeed. The difference with bloke is that it denotes nothing except maleness, although it would not usually be applied to someone upper or middle class. It is not the same as ‘guy’ which in an American context is classless and often sexless. That is why you often here middle class Englishmen using guy; they want to appear classless but cannot bring themselves to use the more working class ‘bloke’.
The really derogatory terms for women are the ones which make distinctions on the basis of being lower class (chav), loose morals (slapper, slag), age (old broiler, trout) and low intelligence (bimbo). There are no male equivalents for these terms.