Your ex is an A_hole. Sorry for the rough words. But here's my advice:
First, don't try to convince your son that his dad loves him. If you do, your son might grow up with all the wrong ideas about love (like, not being there for your kid even when the power is out and you had to go play sports is "love"). If I were you and the boy asked, "Why does dad do that?" and so on, I'd tell him, "If there is something bothering you, talk to your dad openly about it." But that is just me.
Second, have a good talk with the boy's father. A real honest talk. Ask him, does he not realize what he is doing is NOT love or does not prove the love he claims he has for his son? What kind of upbringing did he have anyway? It could be your ex honestly has no idea how to be a father if no one showed him.
Third, look to other men in your family for a role model for your son. Even telling him stories of your own childhood - like grandfather, father, uncle, etc. - and the way REAL men and GOOD fathers act, would help inspire him to be a good father one day.
Most of all, teach your son to learn from other people. When people do good, you learn what to do. When people do bad, you learn what NOT to do. At this time, all his dad shows him is what NOT to do, and how NOT to be a parent. You owe it to your son to teach him to stand up to life's challenges and be a better man than the screw-ups he runs into now and then.
We've tried to deal with people like that. Honestly, if it's a minor flaw, or an occasional thing, talking helps... but only if the guy is the type of man who acknowledges mistakes and wants to improve. Otherwise no. I rarely see real change. But you can try. And for your son's sake, it is worth the try.
The guy sounds like he acts like a dad only when he feels like it. Not a good thing. Good luck and best wishes. You sound like a good mom!