Stillborn children will not have a birth or death certificate, may not have been given a name (unlike now where it seems to be more common to name all babies and talk about them), are unlikely to have had a family notice published in the local newspaper and may not have been buried in a family plot which may make it impossible for you to get the information you are looking for. Have you checked the records of the church the family attended to see if there are any clues? Family Bible? Also, have you tried asking all known relatives? sometimes stories are passed down in one branch of a family but not others.
