Deer and lamb would be good substitutes, but be aware that goat has a UNIQUE taste~ as does deer and lamb. Until you try it, you won't know. It is the taste- and scent- of barbecued goat over an open mesquite fire that brings out the carniverous fangs in a human being. I'm not kidding...talk about drooling; sometimes I can feel my canine-teeth growing as the "cabrito" grills, my canine-teeth extending like a vampire, and I just want to rip into MEAT as our pre-historic ancestors did. It is that good.
As far as the BBQ fajitas thing is concerned, either deer or lamb would be extremely tasty and I would recommend barbecuing either haunch.
I have 3 bone-in legs of lamb in the deep-freeze and the beautiful Mrs. Rivet has told me they are absolutely off-limits for barbecuing. She loves them oven-roasted to a crispy exterior so much that she cannot abide any "experimentation" with them.
As if grilling would be an experiment!
But, she is My Queen and soul-mate. Since we were dating I've made her a roast leg of lamb for her birthday (at least), and that's how she likes it. Thus....no lamb bbq around here.
No worries, we can get goat easily enough and we are both happy.
Give the lamb or deer a try; don't think you will be unhappy.