Coffee and black/green tea are typically considered to be prohibited (I know active members who drink green tea and still participate fully), but caffeine in general isn't banned. One of the apostles even acknowledged drinking a whole lot of diet coke to help while learning to use a computer[0]:
> It took a great deal of time, repetition, patience; no small amount of hope and faith; lots of reassurance from my wife; and many liters of a diet soda that shall remain nameless.
> It took a great deal of time, repetition, patience; no small amount of hope and faith; lots of reassurance from my wife; and many liters of a diet soda that shall remain nameless.
[0] https://www.churchofjesuschrist.org/study/general-conference...