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.
Tip: If you're not sure where your TntMPD database file is, read this FAQ article.
What if two people open TntMPD at the same time?
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. Therefore I haven't felt comfortable using a service like this for my data. But Dropbox handles conflicts like this differently.
If you open your TntMPD database on your computer while someone else has it open on theirs, and both of you make changes to the database, Dropbox will create 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 would then have to use TntSync to merge any changes.
To avoid having more than one person in the database at a time, upgrade to TntMPD 2.1 r24 and turn on the option to "Warn if someone else has the database open". More info here.
Combined with TntSync
If you are a husband and wife team and want the ability to work offline at the same time, you might consider using TntSync. To do this, copy the original TntMPD database to a non-Dropbox folder and then make whatever changes you want. When you're finished and online again, synch it with the TntMPD database in the Dropbox folder. This will make your changes available to your partner, who has also been making changes and can then sync her changes to the database as well.
Another approach to consider if TntSync is too technical for your spouse, than you could setup your spouse to open TntMPD directly off the Dropbox drive. You could have a database stored on your local hard drive that is not associated with Dropbox that you'd use when you're in TntMPD. You'd have to run TntSync occasionlly to sync changes between your local database and the database in Dropbox. This has the advantage of allowing your spouse to not deal with TntSync at all. Plus it allows simultaneous use of TntMPD. The only time the database in Dropbox could possible be used by both you and your spouse is if you try to run TntSync when your spouse is in TntMPD. But TntSync also gets this new feautre, so it will also warn you if your spouse is in the database.
Other Benefits
Another benefit to using Dropbox, is that it saves a copy of everything in your folder to the cloud and on your other computer. So it also serves as a back-up solution for your database and any other MPD files you keep in the Dropbox folder.
What if you have a slow connection?
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.