Hi Christian,
I’ve never rented a motorcycle myself. But I did rent a car from this company Wild Rider CR, which specializes in motorcycle tours and rentals: http://www.wild-rider.com
I also found this company online: http://www.costaricamotorcycletours.com
I don’t know of any rental agencies located in the Southern Zone itself. I think you’d have to pick up the bike in San Jose and then travel down.
For the Southern Zone, most main roads are paved and in relatively good shape. But once you go to secondary roads or if you’re on the Osa Peninsula, you’ll probably want something that can go off-road as the roads will be dirt at a minimum, muddy and potholed at worst. Something to keep in mind.