1. Select "Disable automatic syncing for all i Phones" under Edit / Preferences / iPhone in the iTunes menu.
2. Uncheck "Automatically sync when this iPhone is connected" in the Summary tab of iTunes.
3. Check "Only sync checked items" in the same tab.
4. On the computer you want to sync contacts and calendar, check the corresponding boxes in the Info tab. UNCHECK everything else in the MUSIC, PHOTOS, PODCAST and VIDEO tabs.
5. Sync your iPhone with this computer FIRST.
6. On your other computer, follow the same steps above (1, 2 and 3). Then, UNCHECK everything in the INFO tab, and check everything else on the other tabs.
7. When you sync with this second computer, you may get a message that the iPhone has already been synced with another computer, and that the media library will be deleted. Fine. There should be NO media library on the iPhone since you unchecked all the media items on the first computer, right?
8. Sync. Then you can sync on both computers and each will sync what is checked and not overwrite the rest.