I've not dealt with baby goats but, I can tell you what I do for a calf that won't take it. I gently open their mouth and put the nipple in. Then I gently work their mouth by gently squeezing and letting go. I do that a few times and then give them a break. Usually after a couple tries they start themselves. Also are you using a goat nipple and not a calf one? Goat nipples are smaller and I think a calf one would be to big.
Have you check to see if there is a backyard goat site?????? or I've heard of a goat Joural????? Check out homestead.com?????That might give you some lead. hope everything works out!!
so get you a kid or a lamp nipple.an put it on a coke bottle.an gently rubb the nipple on their mouths.an if they dont open them gently open them an put the nipple in.if you dont have goats milk.whole cows milk will wrk to feed emm.jersey or gurnsey milk is best.
You also have the option of tethering mom and raising kids up to nurse? Get the milk flowing and drizzle on the kids mouth. They catch on fast and usually mom will let them nurse after that.
I would make sure the mother does not have mastitis. Try milking her to get her milk flowing and bring her to the kids. Once they get a taste of milk they all will get the idea.