I don't know of any existing software that can convert the Registrations from the DGX-660 to the DGX-650, or vice versa. I'm familiar with the format used to save Registrations on some of the PSR-E models, and I assume that the DGX models use a similar format, but each model usually has its own particular variation of the format as far as the specific data fields that are saved, how large any given field is (e.g., 1 byte or 2 bytes), and what the range of valid data values is for each field. If someone were familiar enough with the specific format used by two different models, then it should be possible to convert the Registrations saved on one model so they can be loaded and used on the other model, although there might be some data that has to be dropped (because there's no equivalent field on the second model), or that cannot be filled (because it exists on the second model but not on the first), or that has to be given a different value (because the given voice, effects type, etc., is not available on the second model).
Also, on the PSR-E models that I'm familiar with, you can't save the Registrations to a separate file by themselves; instead, they're saved within a Backup or User file that includes a good bit of other data as well. That means you'd need to extract the portion that contains just the Registrations from the first model's Backup or User file, convert it as best as possible to be compatible with the second model, and then insert it into the second model's Backup or User file. Note that there's a checksum field inside the Backup or User file, and if you modify even one byte of data in the Backup or User file then you will need to modify the value of that checksum field accordingly, otherwise when you try to load the Backup or User file the keyboard will see that this checksum value doesn't agree with the rest of the data in the file and you'll get an error message.
So, since there's no existing program for this, the simplest solution would be to recall each desired Registration on the first model, go through each parameter in the function menu and write down what its setting is for the given Registration, and then manually set up a corresponding Registration on the second model.