I have a friend with a father who had a heart attack and still plays table tennis. I myself suffer from serious injuries after a car accident. I think you should be able to play table tennis if you do what the other posters suggested, it is as when starting with any exercises, go very slow in the beginning.
You should not take nor should I give medical advice over the internet though, so take what I say with a grain of salt and consult a doctor if in doubt.
I'm fairly certain that your life is not over just because you had a heart attack though. Having one at 37 must suck, I felt very much the same with my accident when I was around 20, it takes some getting used to, but life very much goes on, you just have to adapt and overcome.
Start at very low intensity and build up _very_ slowly.