I don't have a copy of the DVD of the film Juno, so I can't look there to see if it is in a bottle (that is, a commercial product) or something that is made from a recipe.
However, if it is in a bottle, it may be the product made at one time by the R.W. Knudsen Co. I don't find it listed as one of their current products however.
I don't find any specific recipes for any drink called a "ginseng cooler." I found recipes for ginseng teas and other drinks, but nothing with the name "cooler."
Perhaps someone else replying to your question has a recipe.
You may try to contact the screenwriter of Juno, Diablo Cody (real name: Brooke Busey) through her agent, Sarah Self and ask just what she meant by "ginseng cooler." Sarah Self has just joined WME (William Morris Endeavor Entertainment.) The phone # for WME is: 310-295-9000. The mailing address is: One William Morris Place, Beverly Hills, CA 90212. You may have go "the old fashioned route" and write a letter & send it via US mail. You may or may not get a reply.
Over 30 years experience as a reference/information librarian