I honestly think hospitals are the best idea. Virtually all baby deaths end up at a hospital, but not all end up at funeral homes. There's a lot of options regarding how to handle a child who's already died, but a death certificate has to be written up, and death can only be officially proclaimed by a doctor. Also, cause of death has to be taken into consideration. Hospitals are almost exclusively the end result for deaths at any age.
Hospitals also virtually always have social workers and volunteers. Probably best person to talk to in person is the front desk person for the regular hospital entrance, Not the ER. Also, there's likely a general purpose line for the hospital if you want to call, ask for "Social services."
The vast majority of the time, the hospital attempts to help the family deal with death, particularly in case of the death of a young child. If you offer your gowns to the social services department of the hospital, you can be virtually guaranteed they'll be given away for free (hospitals also do a LOT of free services, such as volunteers, free medication provided from patient assistance programs, and various services from within the social services department).
You may want to just give the gowns to the hospital, or you may want to give your number. If just the number, clarify you're giving the gowns away completely for free, with no strings attached, and the only reason you're not giving them the gowns is you'd like the parents to have the chance to customize the child's clothing (like request a specific color or somesuch). Reason for that is hospitals are usually very suspicious of people trying to take advantage of a distraught family. Sadly, that sort of thing is fairly common.
I worked in a patient assistance program, as a customer service rep, so I've spent Many hours speaking with the social workers for the hospitals and larger doctor's offices. Sometimes they share stories, and some people have pulled nasty things. Hospitals usually are good about referring people to charity things, but often don't mention things that cost money. If they get even the faintest idea that you'll charge for the gowns in some fashion, there's a good chance they'll ignore you if you just give your number.
That is my full, complete, unabridged suggestion :P