I've shot trap with my AR...
But I didn't do as well as I did using a 10/22.
AR: Rock River M4gery with a EOTech. Hit about 50% of birds thrown (3/6). (At a rifle-safe range) Okay, I'll attribute that score in part to "luck". I quit while I was "ahead". Basically one shot/bird. Once it gets too far out, it's almost impossible to hit and recoil recovery on the AR, without a brake, is tough when tenths count.
10/22: With a shortened barrel (to legal minimum) and a 'scout style' red-dot scope and a slicked up action job. Shot birds all day long... consistently hit between a third and a half of all thrown after a five or ten bird warm up. If you miss with your first shot, you can usually get a second or a third if you need it with the 10-22, although the first one is your best one.
And before anyone hoists the BS flag: You can buy the video of me shooting birds from chiefaj.com. He uses it to advertise his "Moving Target Marksmanship" course.
Oh yeah, and I really enjoy shooting incoming clays with an adult-sized Red Ryder BB-gun. In fact, I'm the USA National BB-gun champion, for what that's worth. (Shot 8-10 in the finals on incoming clays).
I'm not super-human. There's "tricks" to doing this. I can also shoot aspirin tablets out of the air with a 10/22 or BB-gun - and I can teach you and/or your kids to do the same, often within 15 minutes of instruction, easily with a half-hour of instruction. Quarters are almost too easy (and expensive!). Paintballs are messy. Charcoal briquets are perfect to teach with.
And I still have plenty of learning left to do. I recommend (HIGHLY) the Appleseed program for those who haven't had it yet (or who've been out of the service for a while). It's worth its weight in gold and it's cheap!
And if you want to shoot trap with a rifle like I'm talking about, Chief AJ will teach you that as well!
I consider myself a very lucky person to say that I've enjoyed shooting trap with a rifle. Few have the opportunity in this day and age to have a safe place to do this.
All the best...
John