Sorry, but you are asking the impossible.
200mA at 5V is only 1W input power, so a maximum output to a speaker of about half a watt, with a class AB amp.
You also need adequate voltage drive to the speaker to get a particular power level; with 5V a non-bridged amp, you cannot get 1W in to a 4 Ohm speaker.
At 2V & 200mA you are down to fractions of a watt.
5V and a bridged type amp may get you somewhere near, if you have an adequate current available.
A TDA7052 would work down to 4.5V and give around 1W max output.
Or you could try two LM386s in bridge configuration, which is rather less efficient.
Concept circuit below.
Note with a built up "bridge" amplifier such as this, the inputs are swapped, so the outputs drive opposite voltages, effectively doubling the voltage available across the speaker. It should still work, at lower power, down to 5V or less.