Your ds can invite whoever he/you allow him to invite. Personally I would certainly not make any of my children invite someone who is essentially bullying them to their special occasion, whether it be a birthday party, first communion, Bar Mitzvah or other special thing.
As for arguments like 'your son needs to learn to be the bigger person' or 'it's not fair' etc. What is fair about the other child throwing stones at your child, what is fair about him effectively being rewarded for his behaviour by being invited?
The other boy isn't being ' the bigger person', your ds doesn't have to invite him to his party to be the bigger person, he just doesn't need to retaliate or bully the boy to be the bigger person. The other boy is old enough to learn that there are consequences for his actions, he should already know this by the age of 9 or 10.
Let's say your dh works in a team of 10 people. Dh and 9 others, working in a team for say 5 years. Over those years it has turned out one employee is a massive bully and spoils everything, but the other 9 have become good friends. If there was a special anniversary/celebration/new baby etc it is likely the other 9 people would like to party/go to the pub for a celebration etc without the bully. If your dh was the bully, would he expect an invitation? If you or your children were the bullies, would you expect invitations to everything?
I would not want a child going to my ds's party with a track record like this child's, especially if it was in my own home. It would be likely he would spoil your ds's special day.
But, if you don't invite the boy, it might be diplomatic to not make it obvious he is the only one not invited. E.g. give out the invitations over 3 or 4 days so it can be done more discretely, maybe ds could quietly say to not mention it out loud when giving them out as not everyone is getting an invitation etc.