I had a baby (well, technically speaking, my wife did) in Sri Lanka.
Government wise, it was trouble free.
Doctor wise, it was harrowing!
But that's another story, let's just say you should choose your doctor carefully.
Paperwork is minimal, just make sure you check in to the hospital with correctly spelled names, and they prepare the one page birth registration for you, either help them with it, or check it carefully, and then take it to the Registrar of Births, where they will give you a Birth Certificate in Sinhala, and translations into English as well, for a small fee.
I'm Canadian, my wife is Indian, and my baby boy had a Canadian Passport almost immediately, thanks to the wonderful Canadian High Commission in Sri Lanka, all we had to do is to give our documents and the birth certificate issued by the Sri Lankan authorities.
Unfortunately, being born in Sri Lanka does not entitle you to be a Sri Lankan Citizen, so I had to pay 100% tax on some land I bought, but now, I guess that is also out the window, and it is near impossible to purchase land in this beautiful country!
Let me know if anybody needs more advise or guidance on having a baby in Sri Lanka.