IMO the best opportunities for SAH parents is childcare. Even if you don't want to take on a kid full time you could do before school time with school aged kids and make $15 - $20 per kid for an hour or so of care! Same with after school care. OR just open up for part-time kids a couple days a week. OR you could be a 'sub' for other in home childcare places. I know a ton of people who are looking for last minute places for their kids if their regular sitters are on vacation or sick themselves. That could pull in easily $30 per kid.
Word of mouth is the best way to go for this type of thing - friends of friends might use you since they know someone you know and who trusts you. I would 'advertise' it on Facebook or similar. Or start asking around for people who do in-home childcare and go meet and speak to that person and offer your services as a 'backup' if she isn't available.
This is very poor advice! As a licensed childcare provider (in home) in the Rochester area there are LAWS against this advice, you cannot just go and be someone's "backup" ??? You have to go through the state to become a substitute for a single person, you can't be several people's "backup" you also have to do a lot of training every year, and you have to be finger printed, with a back ground check, and run through a child abuse network that dates back to age 18 with all your addresses! If you do childcare without a license its ILLEGAL and they will catch you. As a licensed provider with 18 yrs under my belt, this is my career and I don't suggest you follow this advice unless you take on the entire license process!