The ornamental design for a beautysalonchair, as shown and described.
FIG. 1 is a perspective view of a beauty salon chair in accordance with my design;
FIG. 2 is a top plan view of the beauty salon chair of FIG. 1;
FIG. 3 is a front elevational view thereof;
FIG. 4 is a left side elevational view, with the right side elevational view being a mirror image thereof;
FIG. 5 is a rear elevational view thereof; and,
FIG. 6 is a bottom plan view thereof.
The broken lines showing the pedestal in FIG. 1 and the screws in FIGS. 1 and 4-6 are for illustrative purposes only and form no part of the claimed design.