Transimpedance Amplifier and Photodiode for BFSK
The easiest modification you can make to your single rail photodiode amplifier is to reverse the photodiode position and have the anode grounded like this: -



I've also marked on the direction of photodiode current with a red arrow. This circuit would now satisfy the feedback constraints of a single rail op-amp; the output will rise positively from close to 0 volts in the presence of illumination. 

However, do not try and use this with any op-amp; only op-amps capable of working with inputs and outputs at the most negative supply rail will work and the LM324 is good for that.

With your current circuit, the op-amp output would have to fall negatively below 0 volts to satisfy the feedback rules for an op-amp; clearly that is impossible because your circuit hasn't got a negative supply rail and, in effect, the output clamps to 0 volts with no useful signal present at the output.