This is a somewhat stronger method and requires a little less finesse in determining the length of the screw and the angle of entry. Get your helper to stand on the floor to press it down. Apply adhesive on two sides of the block, and position it along the side of the joist under the loose, squeaky area so that it is in contact with the joist and the floor. Screw the block to the joist first. Then screw through the block into floor.
Floor is still up, but is reinforced as strongly as it if was resting on the joist.
Unless you are willing to roll back the carpet, it is tricky locating a joist to screw into. From below, you can predrill a small hole through the floor, say an inch from a joist, and literally push a nail through subfloor and then through the carpet. You can use the protruding nail as a guide to locate the center of the joist from the top by simple measuring. It is useful to have your helper hold piece of scrap wood tightly down on the carpet so that nail will more easily pass through without raising the carpet. You could use screws for this, but I wouldn't advise it because some carpets will wrap onto and snag the screw threads.