There's more political sponsorships and controversies than just state songs.
So here's a few good ones
20 states have their state drink as milk. Just wait for a lactose intolerant politician to have to be a poster child for the benefits of drinking milk. I suppose some of these states don't produce much milk.
2 states have alcoholic drinks: California Wine and Alabama Whiskey (although Alabama does say it's the state spirit)
What about the children?
There's Tomato, Cranberry, and Orange juices. The latter two may be obvious choices(Massachusetts and Florida)
One corporate sponsorship, Moxie Cola from Maine. Haen't heard of them? At least Georgia did not give 'Coca-Cola' a boost.
Kool Aid from Nebraska
and water from Indiana.