S.H.
I have had lulls in finding sitters and then I have had several options.
1. Since you go to church asking someone there if there is a list of qualified babysitters. Either young school aged teens or retired grandmother types. Considering your circumstances (no spouse or family) I would hope a grandma type would offer for free or at a reduced rate.
2. Ask your friends who they use. Sure there will be comments about how moms do not share the babysitter contact info, but that is not all moms. I am always there to help a friend or babysitter find work.
3. Make more effort with your son's friends and the families. Now that he is getting old he can have a drop off play date. You are at an advantage since you only have one child. You could trade off for a night out.
4. Ask the teacher at your son's school. She may know someone or she may even babysit on the side. Also ask if you can exchange contact info with other parents at the center. More people would be willing to reach out if they only knew your situation. Sure it gets old if they feel taken advantage of or if your son is super difficult, but I have a feeling someone at the school/daycare could team up with you to watch each others kids.