Q: Syncing Google Contacts with iPod Touch iOS 1.1.5

I have one of the first iPod touch models ever released.  It does not even support the App store, the only apps it has is the default iPod apps put on there by Apple.  I was always able to sync my Google contacts with the contacts on my iPod whenever I synced with iTunes on my Windows PC, under the info tab there was an option for Syncing contacts with Google, Outlook, and Windows Contacts but after the last iTunes update I no longer see this option available on iTunes.  I have researched this alot and tried all of the other "work arounds" for this like the one explained in this discussion thread:

After upgrading itunes 11.1, sync with google contacts option disappear.

and

how do i get ipod touch to sync contacts w/gmail

and

Contacts syncing with Gmail

but since my iPod is has iOS 1.1.5 and will never be able to upgrade any higher when I add my Gmail account to my Mail app there is no option or "Contacts" button anywhere to be found, I am guessing this contact syncing feature wasn't added until later iOS versions.

So my question is now that iTunes no longer syncs contacts with Google, is there any work around you guys know of that will work with my primitive stone age iOS 1.1.5 iPod touch?

Thanks alot!