Is it possible to use 'must' or 'should' to express certainty in the future? Is the sentence 'He must/should be coming tomorrow.' correct?
Should is never certain; it indicates a correct or expected action to be taken.
Must indicates a requirement.
The only problem with your sentence is that by adding be to the modal verb, must be and should be weaken the certainty, and indicate that the speaker is guessing or making a deduction. I'm not sure when this connotation came into being; the literal meaning of must be and should be is strong, but sometime we started to use must be and should be as a weaker expression of certainty.
The strongest modal verb in English is shall; it's rather formal though.
If you just want to express certainty but not cause, it's fine to say He will be coming tomorrow.