If you play on a computer, then simply unpack the game (0.67) into a new folder and play. The old version (0.66) can be deleted (first in the trash), since Ren'Py stores saves in two folders - in the game folder and in a hidden system folder.
For Android, you can use the file manager to move your save files to another folder, then delete the old version, install a new one, run it and turn it off, and move your save files to the save folder.
This method is somewhat more complicated, but much more reliable and does not depend on the mood of the Ren'Py sponsor servers.
Deimus carefully indicated the paths to the save files here: https://townofmagic.com/faq/
