I do understand what you are looking for. You are not looking for a kid that was kept in the barn and bottle fed along with the others several times a day. You are talking about a kid like (Peanut). He was bottle fed by my neighbor's firend. He lived in her house for a couple of months. He actually wore diapers and truly thought he was part of the family.
I will see my neighbor's this weekend and will let them know. The one neighbor has dairy goats, but does not milk, just raises. My other neighbor raises Boer (meat) goats. I don't know that you care what breed, you are more looking for the circumstance, needing to be bottle fed. It may not be that they are rejected. In the case if Peanut, he was not rejected, it was that his mother had 3 kids and was not able to provide enough milk for all three and Peanut (being the smallest) was not getting enough.