I'm having trouble finding a 220v "portable" air conditioner that's
designed and priced for a bedroom-sized area. I was hoping there would
be a converter box available that could make my American 120v appliance
compatible with my American 220v socket.

You are talking portable AC that can be moved from room to room and not
a window unit ? right ?

I am not sure why anyone would want to fool with those, but many must as
there are many kinds for sale.

Shouldn't you be able to just plug it in ane standart 120 V receptical
in the room ?

Yes, that look like what I'll have to do but I wanted to use the 220v
plug because it's going unused and it's on its own circuit.