You will be doing something tomorrow. You are going to be doing something tomorrow.
I only find the "will" structure in different grammar books, but the second sentence sounds right to me. However, is it wrong?
'Will' is much more common in this structure but 'be going to' is often possible as well, especially if we are talking about a plan and making a prediction with evidence. Both your sentences are fine.
Betty Azar's 'Understanding and Using English Grammar' and Michael Swan's 'Practical English Usage' give examples using 'be going to' in the Future Continuous (or progressive).
Example from Swan: I'm going to be working all day tomorrow, so I won't have time to shop.
Example from Azar: Don't call me at nine because I won't be home. Iam going to be studying at the library.
'You will be doing something tomorrow' is an imperative. Therefore it would usually be a command, issued by a superior. It is a statement of intent. 'You will be going to the store and collecting some parcels'. It implies 'You will, whether you like it or not.'
The second is still an imperative. But it is stated as a statement of fact, rather than a command. It would be what a parent says to a child when a treat is in store. 'You are going to be doing something tomorrow' might precede a look of surprise, followed by 'You're going to the seaside.'
Will is the most common, but since "to be going to" is also used for future intentions/inevitability, it too is possible.
e.g. Next week I'll be relaxing on the beach in Spain. e.g. If all goes well, I'm going to be relaxing on the beach in Spain at this time next week!
I would also be inclined to use shall, depending on the person and the level of force.
Traditionally in Australian English, shall is used for the 1st person whilst will is used for the second and third persons. This is flipped for forceful statements or commands.