EEP!!! I'm two years late for a surprise exam on Middle Earth and Hobbit!!!
Oh well, better late than never
...
By the time of The Hobbit, there seemed to be only two santuaries of Men from which Beorn could have found his mate: Woodsmen village and Dale. Of course, that is discounting the possibility of the random Ranger and wandering Wizard. It may also be possible that some teenage Eldar maiden or bearded dwarf spinster discovered the masculine appeal of the hairy macho man of Carrock.
I certainly find the prospect of Beorn laying with some Eldar entaintaining, though implausible as that would give rise to another line of super-Men with shape-changing elvish lineage.
(How'd I do for my first paper after 3 years of truant?)