Think of the PC speaker as a device attached between +Vcc (usually 5V 
but it can be 3V) and a switch that grounds it periodically (the chipset 
output). Now if you make a programmable small value resistor and attach 
it between +Vcc and the speaker wire that was previously connected to 
+Vcc you have volume control. The resistor can be a PNP/PNP current 
mirror for example, controlled by a microprocessor. That should work 
nicely (excepting for the P=R*I^2 law which you must turn into a log law 
to satisfy human requirements for volume control - for example using a 
lookup table). Maximum expected current is 0.6A which is in range for 
almost all simple low power transistors.

hope this helps,
Peter

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