Well, if male birds don’t have a penis, I’d hate to imagine what those lorikeets I saw at the zoo were doing!
As for the OP, as I understood it, male bottle-nosed dolphins peni are somewhat like a switchblade, and kept inside their bodies for protective reasons until needed. I had read that some species of birds were similar, such as some species of ducks among others. I am pretty sure the author I read that from was Desmond Morris.