Try dry cleaning fluid (tetrachloroethene).
Hook up a wet pickup vacuum cleaner using the crevice tool for maximum suction. Before you put the fluid (or any solvent) on the tape spot, put some on a small area back in the corner of a closet to test whether it removes the color or damages the carpet. Don't apply enough to soak into the backing.
If it passes that test, alternate applying the fluid to the tape spot, let it sit for a few minutes then vacuum the fluid off. The object is for the fluid to liquify the glue so the vacuum can remove it.