http://homejobstop.com/
I did a ton of research on this last year and this is a reputable work-from-home jobs board. They vet all their posters: no scams, no MLMs, just actual jobs for actual companies for which you get paid for the hours you work. They are very realistic: you are not going to get rich from any of these jobs, it will take a month to six weeks to find a job, you will submit your resume to a number of different employers, some will respond, some will not, but in a reasonable period of time you should find a job that is a good match. It took me three weeks. There is a small charge for a "lifetime membership" to the jobs board (around $25, if I recall) but it was totally worthwhile. I'd spend that much paying a babysitter for me to go out for a single job interview.
The job I found: I work for a consulting company, doing quality control for a major search engine. I log onto a website and work whenever I want, 24 hours a day, seven days a week. They ask that I work between 10-20 hours a week. I am paid $15/hour. I am not selling ANYTHING. I am evaluating queries and results based on detailed criteria.
Honestly, with a 5-year-old in half-day kindergarten and an 18 month old, getting 10 hours a week in just about kills me, and a lot of it is late at night, and my husband and I do end up "taking turns" quite a bit, especially on the weekends. That said, I do not have any child care costs, and I manage to earn around $500/month.
This has been a really good solution for our family, but it is certainly not magic - there are challenges, just like any other job, in balancing work time and family time and parenting responsibilities.
Good luck in your job search, I hope you find something that works for you and for your family!
J.