The ornamental design for a supportpost for a towel rack, as shown and described.
FIG. 1 is a perspective view of a support post for a towel rack showing my new design;
FIG. 2 is a front elevational view thereof;
FIG. 3 is a rear elevational view thereof,
FIG. 4 is a left side elevational view thereof,
FIG. 5 is a right side elevational view thereof,
FIG. 6 is a top plan view thereof; and
FIG. 7 is a bottom plan view thereof; and,
FIG. 8 is a perspective view of a thereof, with the broken lines showing of a second post and towel rod being for illustrative purposes only and forming no part of the claimed design.