One application note recommends adding a 20-50 Ohm series resistor to minimize ringing. It doesn't mention where to put it, but I guess right at the gate that generates the read/write pulses?
Nope, in the other end. The output is low impedance, the input is high impedance.

And since I have two FIFOs in parallel, should I add two resistors and use seperate tracks to the FIFOs?

To do the above, you would have to.

The 'easy'ay out would be to use a slower FIFO, todays FIFOs are mainly used in high speed serial/parallel conversions and thus lightning fast.

It MIGHT be an idea to add a small cap from FIFO clock to ground since you are using a '51 the speed is not that great.

Erik