Hi Mark, I realize this is years old but in hopes it could help others here goes. In the manual for the Sharp LC-52LE640U and similar models, there is a listing for Remote Control Buttons that shows RS-232 commands for all the functions of the remote; basically RCKYxx (RCKY32 = Vol-, RCKY33 = Vol+).

It should be noted that in these models, the RS-232 isn't enabled by default, it's poorly documented but you have to first send RSPW1 to enable serial control, I believe you first need to manually turn on the TV.