If I was in his position and friends began calling out of nowhere to hang out I would be embarrassed. He'll know the attention is because of his situation and might feel resentment towards the people that only want to befriend him in a tough time.
Just swing by his place now and again with a six pack or more. Don't steer the conversation towards the bad news just bullshit with him. When you leave don't mention the divorce, wife, kids if they have them, just tell him to have a good one and leave.
He'll know that you're thinking of him and will appreciate the time together without remenscing about bad times.
Hope it works out for him, there's only one couple I call myself friends with that will last the long haul imo. Seems like everyone is getting divorced these days