The coach said that they _________ to the gym every day next week to get in shape for the tournament game.
- should go
- will go
- will be going
Any of the three options work. The sentence is reported speech. The reported speech includes the phrase "next week", which–when used properly–refers to a situation that has still not happened at the time of the reported speech. Since this is the case, the modal verb will is fine; it can, but does not have to, be backshifted (to would) in this case. Thus, both 2 and 3 are okay. 1 is also okay in this context.
If, on the other hand, the time meant by "next week" is already over when the sentence was said, then the phrase "next week" should have been changed to "the following week" and any present tense verbs, including modals, backshifted to the past tense. In this case, will would become would in both 2 and 3. Should would still work, because it cannot be backshifted.