Maybe this is your problem:
Many developers when they updated their apps to support iOS 5 and 6 dropped compatibility for iOS 4.2.1 and earlier.
Your only way is if you have the version that was compatible on your computer such as in the recycle bin/trash or in a computer file backup. In that case delete the current version that is in your iTunes App library and replace it with the older version. Then sync.
You can redownload iTunes purchases on your computer (you can on iPod if you have iOS 4.3 or later but the 2G only goes to 4.2.1) by:
Downloading past purchases from the App Store, iBookstore, and iTunes Store
However, as discussed above, the version in the App store my not be compatible with your 2G