Although the program does not allow for writing to a file it does give you a way to export the data. Email! Just write a program in AI that will extract all the data from the tinydb and use the delimited text output as the main text portion of the email. This program can be made with all the instructions on how to backup the end users data.
Then you could do one of two things. First you could just have your customers copy the email to a text file and name it something specific like myprog_backup.txt and copy it to a specific directory on the sd card. Or second you could have the program email all the info to you, and you create the file for them and email it back to them as an attachment.
Then with your new program written in b4a, put a messagebox that shows up at install that instructs the person on how to back up the information from the old program, and when they click ok, sends them to the download location in marketplace to the backup utility you wrote in AI. Then the b4a program once the file is in place could read the file and use it to populate your new db and then bing bang boom, your information is backed up. Then no pissed off customers. I know if I had to either lose all my info or copy text from a email, Id copy the text.
P.S. As I was writing this, it occurred to me that there might even be an easier way. I know when I was researching for another program I was working on, that php can write files to the computer that it resides on. You could write a webpage in PHP, and host it on a computer of your own. Then write a program in AI that logs into the site and uploads the database info to the server. Then the website would create a text delimited file, and name it myprog_backup.text, and then using the persons email they provide, email the file as an attachment back to them. This would be completely automated and take away the need of the end user using a computer to do the transfer, as all of this could be done on the phone itself.
Well thats all I have right now, but between those two ideas you should be able to come up with something. And before you ask, no, I have no idea how to write a php site to do this. I never got into php. But I do know it has the ability to write to files on the computer it resides so you should be able to research it and find out how using google or maybe someone else here can help you.
I hope this has helped you or at least given you an idea on how to fix your problem.
Thanx
George