My son-in-law was a part-time DJ for a successful company in our area. They focused on weddings. This involved the company contacting wedding planners and participating in bridal "expos".
Most of these shows take place on weekends - for that matter so do most weddings, so it should fit right into your part-time schedule. I'd start out by attending a couple of the expos just to check out your competition and what their costs are (don't worry, many of the brides-to-be bring along their prospective husbands. Take along a female friend and you won't look out of place) This will give you an idea of what you can charge. I know the company my son-in-law worked for charged several hundred dollars - heck..they paid him $250 per gig plus he got tips.
See if you can work with wedding planners as well. You can Google "Wedding Planners in (your city) and get a list. Start with a phone call and sell yourself. Ask if they also do events other than weddings that could use a DJ. Offer a booking fee as a commission to them.
If sales isn't your strong point, contact other DJ outfits to see if they can refer jobs that they either don't want or can't handle - offer a referral fee as a bonus to them.
Look into joining a trade/barter exchange. They will market your services to their members. You will be asked to accept trade dollars, not cash, for services you provide to their members. After completing a job or 2 on trade use the trade dollars to market yourself for cash clients. You will be able to make purchases using your trade dollars.
Doing a few trade gigs will help you develop a client list to use for reference. Before you join talk to the exchange to see what they have for advertising.
After joining an exchange be proactive with your trade account. Do not let yourself get trade heavy or go to far into debt. You have to manage your account to make it work for you.
If you have any questions feel free to contact me. I can help you get to a good LOCAL exchange.