Is it safe to have one alcoholic drink (i.E. A beer) in between two back-to-back one-hour sessions of tennis?

Not a great idea. Alcoholic beverages are dehydrating. The effects of drinking are individual and can be affected by your age, your fitness level, and how intensely you are playing. At the minimum, your performance will suffer. You are also increasing the risk of heat related illnesses.
Probably. Just stay well hydrated during your games. A single alcoholic beverage, if you are well hydrated, shouldn't have any adverse effects. This is assuming that you don't take any medicines that would interact with the alcohol.