'Coming' and 'upcoming' are not synonyms. Your phrase should be 'in the coming years'. This is a correct and long-established expression. It is an adverbial phrase meaning 'in the future'. The more modern word 'upcoming' is an adjective, generally used to refer to events and planned occasions which are due to take place, for example 'the upcoming elections'. 'Upcoming years' is wrong.

Both are correct but for me it sounds right to say "in the coming years".

Either phrase will suffice.

I would say "in the coming years".