I am trying to make an FM receiver. I have a radio transmitter and it's able to pick up and demodulate the signal from that when the transmitter is beside it, but the problem is when I try and pick up any other radio stations. The variable capacitor is between 10 pF - 60 pF maybe is this too narrow of a range? or would there be another reason for this?
A simple home-made AM receiver, covering the FM broadcast band (88 -108 MHz), can be used to tune in to and receive FM radio stations, through a technique called 'slope detection'.
When a station is off-tuned on such a receiver, either slope of the frequency response of the tuned circuit would convert the FM signal to AM and thus enable demodulation.
Nearby strong stations would make the job easier.
Stations, with rated power ranging from 1 to 10 kW and located 6 km away (as the crow flies), are received fairly well, using this simple receiver.
Stations with higher power ratings, located nearby, have been received with similar receivers even without using the 1.5 V cell.
High 'Q' tuned circuits are a must for such receivers.
Should you be lucky to have high power stations nearby, here's a good resource to build a number of simple FM receivers.
I am trying to make an FM receiver. FM receiver not picking up any stations
The circuit you have posted is an AM receiver and it ain't a very good AM receiver either. You need to load the diode detector (an op-amp input is nowhere near good enough) so that it properly half wave rectifies but, of course, it'll be a bit rubbish on FM.
Delving deeper, it's impossible to say that it is even tuning in the range 88 to 108 MHz because component values are not shown and, critically, construction details are neither.
Finally, you need to DC bias the op-amp input at about half rail for it to stand a chance of working on AM. Plenty of problems to fix.