A photodiode is not what I would choose to use in this circuit. It takes a fair amount of gain after it, in a circuit a bit different than the one presented. There are problems with it, as pointed out by MarkT in post 5.
You could probably use a phototransistor without the use of an Op Amp. As long as the LED and phototransistor are well-shielded from outside light. With the proper amount of LED current, aiming correctly, and the proper selection of a collector resistor, you should be able to get less than 1V unblocked, and nearly 5V as the coin passes.
Take to heart everything up to and including post 5. As suggested, fix millitime now, you -will- run into a problem. It'll be intermittent at first, and again as suggested by then you may have forgotten.