How do you transfer Zen garden to a new computer?

Maybe the easiest way is just to re-download it:
https://www.lexaloffle.com/games.php?page=my

(if that doesn't work, try adding the email you used to buy the game as "Alternative Email" in your profile settings. You should see a list of games you own.)

If you'd like to keep your old player history files, they are called 1.sol .. 5.sol and you can find them here:

Windows: The same folder as the game (e.g. c:\Program Files\Zen Puzzle Garden)
Mac OS X: your_home_folder/Library/Application Support/Zen Puzzle Garden

After you install Zen on the new computer, you can just copy the .sol files over separately.