I wouldn't mind having a babysitting to use every Friday night or so, but not sure you can really depend on it. You could offer to sit really cheap and someone may take you up on using you every Friday even if they don't really need you they could take advantage of the free time if you would do it for a very cheap amount. I would bet a single mom may need your help.

I know this isn't exactly what you've asked. I'm really picky about who I leave my kids with. I've never allowed anyone who wasn't a good adult friend or relative to watch my kids. Here are some suggestions/things to think about and also things that I would be looking for in a babysitter and whether I would hire him/her on a regular basis.

Write up a flyer that is equivalent to a resume/cover letter - name, address, phone number. What are your qualifications? Are you responsible and dependable? Do you have experience? Have you had any CPR or child care training? What days and what hours are you available? Do you have some people besides your mom and dad and other relatives that would give you a character reference? Do you have transportation to get to and from the job or do you need to be picked up? Will you play with the kids or will you pop a video in and have them watch tv the whole night?