Green’s Dictionary of Slang

1. (orig. US) a lecher.

1820		‘Greatest Old Ram in this Neighbourhood’ in C. Hindley Curiosities of Street Lit. (1871) 38: Mr — [...] is much addicted to wenching and that he is known [...] as the ‘old ram’ or ‘billy goat’.
1856		Life in Boston & N.Y. (Boston, MA) 25 Oct. n.p.: A lascivious old Dutch billy-goat [...] wished to dip into the sweets of a young German girl (sweet sixteen) .
1867		G.W. Harris Sut Lovingood’s Yarns 261: The cussed ole billy-goat jis’ sot in tu lickin his lips.
1930		N. Lindsay Redheap (1965) 195: ‘I’d gie him dodderin’ after the wimmen, when he ought to be trem’lin’ in fear of Almighty Goad, the randy old billy-goat’ .
1949		L. Hughes Tambourines to Glory I vi: Tom cat! Billy goat! You big brown bar stud!

2. a boyfriend.

1859

in N.E. Eliason Tarheel Talk (1956) 71: Do you still attract the ‘sparks?’ ‘Johnny horses,’ ‘Billy goats’ and Tom boys?

3. a bearded old man.

1878

J.H. Nicholson ‘Bunkum in Parvo’ in Opal Fever 115: Now listen old billy-goat.

4. (orig. US) a bad-tempered man.

1958

A. Sillitoe Sat. Night and Sun. Morning 177: I’m a bloody billy-goat trying to screw the world, and no wonder I am, because it’s trying to do the same to me.