I tried Google for solution and found a solution that made you copy an ID across but that didn’t work for me on iTunes 10. So I started messing about and came up with my own solution:

1. Create a backup of your whole iTunes on your second computer (the one which needs to be synced with iTunes).
2. Make sure iTunes is closed on both computers. Start by copying the whole iTunes folder from the first computer and pasting it in the second computer replacing any files and folders (if you have music in second computer, don’t worry, you can re-run iTunes lookup to get them back in).
3. Open iTunes on the second computer and plug-in your iPhone. (all your settings would have been copied over with the songs. Re-run the lookup if you have songs missing).
4. Sync away…. you can right-click on the iPhone and click “Transfer purchases” to authorize the second computer. (Please note you can only authorize 5 computers.)

I still don’t understand why Apple can’t do this themselves!!