Designing an amplifier to drive a speaker
This will work off of a 9V battery. Probably would be nice to add another pot for the VBE-multiplier. But it isn't in the spec, so I left it out:



simulate this circuit &ndash; Schematic created using CircuitLab
The above will accept an input that almost meets your specifications. It was designed to actually meet them, but given resistor tolerances and considering it's maximum gain is a little higher, it probably can only be said to handle \$900\:\text{mV}_\text{p-p}\$. The voltage gain is up to 14.8 dB, but can be easily dialed down with the potentiometer you asked for. If backed off to about 12 dB, then it will handle \$1\:\text{V}_\text{p-p}\$ even with the tolerances, I believe. And deliver up to a quarter-watt into the \$16\:\Omega\$ headphone/speaker. (Dissipation in the BJTs is well within their capabilities.)
Reasonably fresh batteries, only, when expecting maximum output!