Hi there, interesting question

I'm glad for the clarification too!
I think you've gotten some really good suggestions here - finding social situations, commerce networks, and other ways to network directly with your target market is an excellent way to provide some education and outreach while getting your name and services out there within that community.
You might consider also placing an ad in your local Baptist or Christian churches newsletter (if they have that kind of advertising?), a neighborhood newspaper, etc. Many church groups host a business-person's-type networking group on their own...check around and see if anything like that is available in your area.
Also, you might check for paid ad space in an e-newsletter targetted to either of these communities. I'm sure there are plenty of really extensive mailing lists with ad space to sell!
Another way to approach it is to personally go to the establishments you're interested in working with - if you know of a Christian owned office building or store, or an African American owned company - go in there and introduce yourself, let the owners know *why* you're interested in working with them andwhat you can do for them. Even if it doesn't result in a contracted client right away, you're actively marketing to the people you wish to work with and introducing yourself along the way. And do leave something behind like a marketing packet or even just a business card or pen (great idea by the way!)
Best of luck and keep us posted on which methods you find work best in reaching your target market.