How do I transfer the iTunes information from one computer to another

my wife has a iPhone 3G with the old os 3, has not upgraded because she is using a older Mac to sync with. I just bought a iPhone 5 and she wants to use my old iPhone 4. Unfortunately the 4 does not sync with her older Mac OS and the 3 does not sync with my newer OS on my desktop. My question is how can I get the iTunes info off he old computer to my newer computer. I do not use iCloud.

Any help would out be appreciated.