Check a couple rescues. There is a place in Upper Marlboro (down Croom Road) called the Unicorn Center that rescues animals, they are VERY nice people. They have a few goats to choose from that need some TLC. Where Magic Happens! (Unicorn Center Inc.)
I know someone who sells goats that has some bottle babies that are VERY tame if you want pet goats. PM me for the contact info. if you are interested.