One solution you might consider is "Dropbox" (www.dropbox.com). It provides a free service up to 2 GB of data, and if you need more space you can pay for it. 2 GB will be large enough for any TntMPD database (which coincidentally is limited to 2 GB as well). Dropbox works on Windows, Mac and Linux. You point it to a folder on your computer, and a folder on your second computer (the one you want to sync with). Dropbox keeps the folders in sync over the internet continually. You can keep other documents in this folder as well, such as your documents, spreadsheets, prayer letters and presentations used for MPD.
If you're not sure where your TntMPD database file is, read this FAQ article.
I've tested some other similar services, and in my experience they were not a safe option for TntMPD. If two computers would both open the TntMPD database at the same time, the last person to close TntMPD would overwrite any changed made by the other. I don't feel comfortable using a service like this for my data.
But Dropbox handles conflicts like this differently. If one person has TntMPD open, and the other person tries to open it at the same time, it will block access to the second person. They will have to wait until the first person is done and closes TntMPD. Because of this it is probably a fairly safe solution to storing TntMPD
in two locations.
If you are offline (not connected to the internet), you can open the TntMPD database file even if someone else has it open. But if the other person changed it on Dropbox since you opened it, Dropbox will created 2 copies of the database (naming them according to the users who saved them). This is good, because it means no changes are lost. But you'd then have to use TntSync to merge any changes.
If you want to maintain the ability to work offline at the same time, you might consider using TntSync. You'd copy the database to a folder not maintained by Dropbox, and you'd synchronize it with the folder maintained by Dropbox. You'd want to limit the times you run TntSync to when you are connected to the Internet.
It also seems that Dropbox is intelligent in how it syncs large files. If you have a very large file, and yet you only change a small amount of data, Dropbox only has to copy the small part of the file that changed. This is good news if you have a limited connection speed, or if you have a large database.
Another benefit to using Dropbox, is that it saves a copy of everything in your folder in the clouds, so it also serves as a back up for your database and any other MPD files you keep in there.