Is there any painkiller as strong as morphine which won't

I've never had constipation problems from morphine but try things containing oxymorphone. Opana is pretty popular.

You're not going to overpower an opiate with laxatives. It's like unplugging a toaster and then shouting at it to make your break crispy. On a related note, that's exactly what anti-diarrheal medications are doing. They're unplugging the toaster so you physically cannot poop bread. Wait I think that analogy got fucked up at the end.

The only other alternative you have is a local block if the pain is coming from an isolated limb or something. Otherwise you're SOL on this one.