You didn't mention it in your question, but I'm assuming that the charity is most likely using an ISP for domain hosting. If that's the case, there's not much you can do as it'll be nearly impossible to get one machine to see the other without making the charity go through the complete hassle of hosting its own domain with all of those management and security headaches or requiring something like SQL Server to run at the ISP.
What you may be able to do is save out the day's changes to a file and e-mail that file over to the other machine. On the other machine, it could look at its day's changes and attempt to reconcile the differences. It's not a great solution, but would be a lot easier and cost the charity less money.
This was first published in December 2002