Mountain bike trainer tires
On a trainer that supports the bike, normal tire rules do not apply, as the tires don't have to support the mass of you and the bike, nor provide any lateral grip.

How narrow tire you can drop down to depends on the actual width of the rim, not the width of the original equipment tires. You can probably fit a tire that is not much wider the the outside width of the rim.

I've run a 1.5" hybrid bike tire on a MTB wheel on a trainer with no issues.