Does AGI recommend any generators to use with my SuperSting™ AC/DC Power Supply?

Short Answer: Yes. The Honda eu1000i generator.

Long Answer: We have had great success with the Honda eu1000i generator (pictured below). It can run for more than 7 hours off of 0.6 gal of gasoline. 

We are on our second generator. The first one ran daily for more than 10 years without servicing or any problems.