A retired English teacher has written this useful advice:
"While it's not a strict rule, generally we say 'happy with' a situation, something that continues for a while; you are satisfied or content that the situation is how it should be. So you can be happy with your job, happy with your marriage, happy with your child's school.
"We are 'happy about' specific events: happy about my promotion, happy about my daughter's marriage, happy about my son's excellent exam result."
There's a pretty good discussion of this point here: