Is it possible to make a square wave generator with a single supply op amp? I've seen ones with dual supplies but I'm not sure if it will work for single supply.
You don't need to use a "single-supply" opamp. Any opamp will work with a single supply if its input is biased at half the supply voltage. Even a lousy old 741 opamp.
Providing you don't use an op-amp that suffers from phase inversion (e.g the TL07x/8x series), you can wire it up the square wave oscillator like the bipolar version connecting the 0V node to either +V or -V. You'll have to accept that unless you're using a rail to rail op-amp the output won't reach either supply rail.