Is the dog a puppy? I know sometimes older dogs will get really frustrated with puppies, because they don't know when to stop being a pest, and they have little needles for teeth.
Does Max seem like he wants to play with the dog at first, and get sick of him, or is he disinterested in playing from the start?
You might also intentionally keep them apart but in view (maybe a baby gate?) and let Max 'ask' to play with the other dog. This might allow Max to build some interest in playing with him and not feel like he's bombarded.
Does your cousin's dog come over to your house, or you over to his? If it's at your house, he might be a little territorial, or like his space is being invaded.. possibly take them outside and let them hang out on the leash in the yard for a little while, bringing them both inside at the same time after they've greeted eachother for a fair amount of time.
Hope that helps a little, or at least gives you a place to start
