Having the source code is good, so at least you will be up and running the program again.
I don't know about backing up data on CoDeSys 2. I believe v3.5 (e!****pit) has an option to save data from the PLC to a file on the PC. I haven't used that yet, and I do not know if it carries across to different firmware versions.
For smaller programs where all the data in the PLC are settings that can be configured from some form of HMI (web visualisation or other) I have done screenshots and restore manually from that. This becomes cumbersome on large numbers of parameters (I have done many with hundreds of parameters, some well over 1000, no good fun) and impossible if not all of them are accessible from the HMI.
I have made some q&d programming on larger systems with many parameters where these were saved to and restored from csv format files on flash memory / sd card. Backup/restore via ftp to&from my laptop/pc. Being limited in available time my work on that was neither pretty nor robust but it can be done.
You may ask your local Wago representatives for help. I find over here they are knowledgable and very helpful.