You probably have rough, 2x framing (stringers) and rough plywood risers and treads with the carpet right on top of them. My guess is that the risers and treads were installed with nails only. I always assemble these with glue and screws at all joints. The nails holding your treads have probably lost their grip in the 2x stringers as the stringers have shrunk with age as they dried out. The nails go up and down a little inside their holes with every foot-fall and make their sound much as a violin bow on the stings does. I would try to use "liquid nails", or equiv. construction adhesive from a calking gun to glue each joint from underneath the treads. The best you can do is to probably use it like calking where the stringers meet the treads (two joints on middle stringer - both sides - and one at each end). This might help but it might not. The only sure-fire way to fix it is to remove the carpet, partially loosen the treads by hammering up a little from below with a hammer, sneaking a bead of construction adhesive between the tread and the stringer, and using SCREWS to re-secure them. This is a larger job than trying to fudge it with half measures from below, but it is more likely to work if the fudges don't work.