First Lisa, are you in California? If you are then it is one of the states where you can request a birth certificate not just a death certificate. Here is an article on it:
I'll see if I can find the info for you on how to do it.
if you want a keepsake one instead you should probably ask on the loss forum if anyone has done one, we never did and while I can give you the websites of some people that will do them, I don't know if they come out nice or not.
Here I found some info, this is a web version of the actual form, you have to go back and download the form as a PDF if you want to fill it out. Only parents can request one.certificate of stillbirth California
Just wanted to add another hug. I know this is such cold info to be posting, but I also know how important these little things were. Thinking of you and sending love along with weblinks.