Is it possible

to genetically engineer people so that, instead of lotsa pain, childbirth gives you the most intense orgasm ever? (maybe also for passing kidney stones)

Perhaps, but that would require completely renetworking the human brain so that ALL pain was orgasmically good, and then we'd die out from masochistic Darwinism (or some shit like that).

Coupled with the practicality of the system, I have to say no.