I work at a store that sells a lot of clothing items

Nah... just be honest. Tell them the back room is empty and say "If it's in the store, it's on the floor."

I work in the clothing department of a local store and I typically just tell the customer that everything we have is on the sales floor (which is most of the time true).

Usually if you tell them no. The next request is, well can you go check, so might as well take a short break while you're pretend checking stock.