I had two skittish 3 month old kids and it took about a month for them to get warmed up to me. I went out there every single day and just sat on a hay bale and read for 30-45 min. I did not look at them, and made no moves to pet them if they got near me for about 2 weeks. I would keep a bucket of treats in between feet so they were forced to come to me if they wanted it. Slowly, I would put a hand on them when they were eating out of the bucket. It took a while but now they love to have their heads scratched and will come running anytime you call them.
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They love everyone. Once they started to take treats from my hands I would bring people out with me and have them stand there while I fed them. Then later they would give them treats. Now when we have parties, there is a line of people waiting to get to the "petting zoo". They get a handful or corn and the goats go nuts. Just like dogs, they need to be exposed to as much as possible to make them good pets.