In the "Shop" section there is an "authenticate" button. Press this button.
You want to type in the same email address, here, on both devices.
You should get two emails, one for each device. Respond to both of them.
At this point, the Song Store, should know that these devices are owned by the same person.
Then, you can "purchase" the songs you already own again... It may seem like it's going to make you pay, but eventually it says "You already own this song, would you like to download it."
Once you have finished this, you may want to "De-Authenticate" your first device... so in the future you can do this again (only two devices are allowed on a single email address).