A few more details would make it easier to provide help. There are a number of alternatives, but the details will vary based on, among other things, what form your "database" takes.

Is it a SQL database on a web-accessible machine? If so, it is (in theory) no different than if the database was at the "other site" on a machine dedicated to the database server -- a common setup.

You could provide your data in any number of XML formats including RSS.

If you provide specifics, you'll get some very specific suggestions here.