I disagree, the links provided DO help. Mainly this one :
http://www.faqts.com/knowledge-base/view.phtml/aid/4058/fid/27
Two listed there will allow for your own domain, here's a direct quote :
"http://www.portland.co.uk/ (allows your own domain name)"
Granted no database is available there but another link exists in the above that could help, which is :
"Here's a host that offers a free database : http://www.freesql.org/"
That combo should meet your unfortunate needs (I say unfortunate as you're asking for a lot). Also, if you're doing an open source project, sourceforge.net is a possability.
I doubt you'll find anything other then the above.