i didn't said to use an arduino, on the contrary i said to choose the best uC (price-wise). So that you can interface a rotary encoder as well. Anyway.
With the 555 you can achieve either a 1-shop operation or continuous operation. In one shot, the resistance will change every time you press and release a button. A 10K pull-up resistor is connected to the UD. Also, the collector of a NPN is connected to this UD. The emitter goes to the ground. The DOWN button is connected to the base of the transistor through a 4K7 resistor. So, when the UP button is pressed, the UD is HIGH, when the LOW, the UD is LOW.
Now, the 555 is an one-shot circuit. Both buttons (up and down) control the gate of the 555 through a diode (so that they do not interfere each other). The output of the 555 is then driven to the INC pin.
For continuous operation, keep the UD transistor connection the same. Then connect the 555 as a multivibrator. Drive the output of the 555 to the INC pin through a second transistor switch. Both buttons control this transistor switch though diodes.
Again, i do not see anything elegant with the 555 - It is a bulky circuit with many limitations. A uC circuit would be like this: Connect the buttons to an input, 2 outputs to UD and INC, make a software filter and.. end. Plus, you can se the uC to operate with the classic initial delay, you know, when you press a button to increase the volume, the first click increases once, then there is a delay of 1 sec, and if you keep pressing the button the volume increases once every 200mSec... It is a hybrid of the 2 previous circuits, one-shot and continuous.