If a pilot is trying to complete 3 day or night landings every 90 days in a multi-engine aircraft in order to be multi-engine current per FAA requirements, can those landings be done in a Simulator or a Flight Training Device?
Yes, as long as the simulator is properly certified (to level B,C,or D) you can do your takeoffs and landings to regain currency.
Long haul airline pilots frequently have trouble staying current for 3 takeoffs and landings in 90 days. This is because it takes 4 pilots to complete a long haul flight but only 1 will get the takeoff and landing.
3 trips a month is about all you do, and if you are scheduled to be the augment pilot, you don't get a takeoff and landing.
It can be done. As mentioned here:
(2) The takeoffs and landings required by paragraph (b)(1) of this section may be accomplished in a flight simulator that is—
(i) Approved by the Administrator for takeoffs and landings, if the visual system is adjusted to represent the period described in paragraph (b)(1) of this section; and
(ii) Used in accordance with an approved course conducted by a training center certificated under part 142 of this chapter.