Not really, there isn't.
Caffeinated drinks or beverages might be more accurate, but that could include energy drinks, pre-workout supplements, a lot of other hot drinks that might contain coffee such as Mochas, etc It also becomes a problem when you introduce decaf cofffee or decaf tea. Redbush tea has little to no caffeine, so this won't work.
While it would be technically correct and understood by most, you might come off as a little awkward or pedantic asking someone if they want a caffeinated beverage in day to day use. I would expect to see the term in more scientific/academic/informative contexts, e.g. "the average temperature of a caffeinated beverage"
If you really need a word or phrase for day to day use, here's a few more colloquial alternatives that would work in the UK:
- "a cuppa?"
- "a brew?"
- "Tea & Coffee?"
Though none are standard aside from the last. They're mostly subjective, and vary from region to region.
Or more simply, just ask if they'd like a drink
But there is a specific whimsical beverage if you're looking for a joke:
- 2 tablespoons coffee
- 6 tea bags
- 64 ounces water
Read more: http://www.food.com/recipe/teaffee-247421#ixzz1eiMHGECp
However, this is a strange term that most english speakers will have never heard of, and you won't find it in any dictionary.