Cat problems

My neighbor's cat keeps shitting on my lawn. We plugged fence holes, put up chicken wire, left water bottles in the lawn, bought spray, put out chilli powder and did everything an old wife will tell me. My friend says hurl the shit at their house but that's not my style and I don't think it will stop the thing.

Talked to neighbor they say it's cruel to keep a cat inside. This has been going on for a long time. Now pregnant family member won't come over because of some disease in cat poop and I'm at the end.

I like cats. I don't want to harm the thing. Can I use live traps and give to the SPCA? Is there a gov agency I can bring a cat to? Surely someone has dealt with this successfully before?