I modified the circuit in the previous post by removing the 555 timer clock input and adding two switches so I could manually increment or decrement the value. These sent a signal to a 556 Timer chip (dual 555s) setup in monostable fashion to send a distinct pulse to the "clock-up/down" signals of the 74193. I also wired the "borrow" output of the first 74193 to the "clock-down" input of the second 74193 so it could count backwards. As inactive inputs to the clock up/down should be high when not in use I sent the 556 outputs via a 7404 hex inverter.
On the monostable circuits I used 8.2K resistors and a 10μF capacitors. I tried a 47μF capacitors but the pulse length was a little too long. With the 10μF capacitors I am getting the occasional double clock pulse, so it would sometimes skip 2 counts. I hooked up my oscilloscope and it looks like I have some noise on the output pulse when triggered. I'm not sure what's causing this so any ideas would be much appreciated.
Update: the circuit noise I have read is due to the switch contacts bouncing and to fix this I need a debouncing circuit.