I understand that Autism is different for everyone, so please don't mistake my request as stereotyping. I am just looking for a broad spectrum of suggestions.
My 8 year old is on the spectrum and exhibits a lot of negative behavior, especially for his age. I have noticed that he seems to get a thrill by saying and/or doing extreme things and picking on his younger brother. For example, me, my wife, his brother and a neighborhood kid were all playing basketball and he would only participate by trying to take the ball from his brother. I was trying to include him without making it into an issue. Then he made up a song about him touching his anus and began to sing it loudly.
He often engages in this type of behavior. We try not to "feed" it but it comes up time and time again.
I think that part of the issue is a lack of positive attention, something which I try to make up for by being effusive when he is good. My wife suffers from depression and sees the negative and often doesn't see the positive (unless I make a point of it). Otherwise she is a wonderful mom and showers our kids with love. But despite that, my 8 year old is always hearing about what he does wrong until, I fear, it's becoming part of his identity. I think my wife's depression has her seeing the negative in very exagerated ways and often reacting very intensely.
My idea about turning this around is to find something he is good at that I can do with him so he can understand that positivity and accomplishment run so much deeper than the thrills of "trolling". I also feel perhaps 50% of his "misbehavior" is often the result of not understanding what is emotionally appropriate.
He is very into Minecraft and Roblox and using stuff like "command blocks" to do impossible things in the games. For a while I tried to spend time programming with him using Scratch but it didn't hold his interest. I would prefer something active that doesn't involve a screen. However I also have bad knees and can't really run or jump.
So I am looking for suggestions on some activity or sport that he might enjoy and become good enough to feel proud. I have tried most of what I can think of but he is either not interested or gets frustrated and has a meltdown. Any suggestions are greatly appreciated.