The top diode never conducts because it is always reverse biased. Try connecting the 0V end of R3 to 4.5V.
What do you mean by +/-200u, don't you mean 200:mu:A?
For a start use a single 741 instead of the quad. You could also consider using a lower current opamp like the MC33171, even then you'll need to increase the resistor values by a factor of 10 but you'll be at the mercy of input impedances and bias currents.
Somehow I don't think this is possible, if you're worried about battery life then use a rechargable or mains adaptor.