The only thing you can do is to encrypt the data as it enters the database, and then decrypt it as it returns. To do this in a semi-supported way, you will need some level of database access, where there may be encryption / decryption so that your main application does not worry about it.
I am not very good at PhoneGap, so I'm not sure if there are any existing plugins that do this. But if you do not mind that encryption / decryption is related to your application code, you can simply pass everything through the encrypt(myData) function on the way to the database, and then through the decrypt(myData) function on the way out. This will work very well if you are only going to / from the database in several places.
This is a pretty tough decision, but, as you said, the options are pretty limited.
Finally, I would suggest using a device identifier (if you can get one) or some other way for each key or each device to get an encryption key, so that each device is more difficult to crack, and not all devices using the same key. A hash of a username or salted username or salted hash of a hash file may be a good option.