J has a few activities but they've taken some finding, and I've had to provide information about AS for the instructors and talk to them before enrolling him so that I could feel confident they'd be able to manage with him, and him with the activity. We've been lucky to find instructors with knowledge of AS, even if it's at a basic level, who are willing to learn more.
He's been having swimming lessons for three years (he's seven) and until recently I'd take him for an extra session, just the two of us. TBH he learned more with me 1-1 than he did in the lessons, and his first instructor was a monster who believed he was misbehaving deliberately to annoy her. He moved on to an instructor who is dyslexic and has empathy with childen who have coordination problems and was able to encourage him appropriately. His behaviour has improved the longer he goes to lessons.
He's been doing karate for over a year and loves it, with the help of very understanding and cooperative instructors. Enquiries at other classes showed just how little some people know about 'behaviour disorders' and I just knew instantly that this was the one for him. He's managed to get his red belt too, although he does struggle with concentration at times and can find the lessons difficult.
Football training is pretty lousy, he can't play for toffee and keeps wanting to do karate in the middle of it. His coordination is poor so he can't keep up with the others, and this can upset him. However, once again we have an excellent coach, disabled himself and with interest in children with special needs, and he has boatloads of useful strategies up his sleeve to help manage J's difficult times, eg letting him be referee and blowing the whistle etc.
We're also trying horse riding now, which he loves. Apparently the motion of being on a horse can be soothing and therapeutic for some children, so it might be worth a try.
I'm now thinking of lunch clubs at school as well (he's just started KS2 and they didn't have any for KS1 in J's school), to help with social problems during unstructured times.
Hope you find something that suits, BH. Brownies might be OK after investigation of local clubs, they're usually quite structured and that might help.