Hi,
I've just had a quick look over the datasheet for the 7216A, and I see that the application circuit has 2 'rotary' switches, and 4 'dip' switches. Looking at the block diagram, it 'looks' like there are only logic signals flowing through the switches, no analogue. so I think that a couple of multiplexers will do, controlled, either by a microcontroller, or with a binary counter (with a push switch as the clock to increment it).
Some IC's you could use are.. 74HC150, 74LS151 , 74LS153 - a dual 4-1 multiplexer.
Although, whether you use a 'multiplexer' or 'demultiplexer' depends on which way the signals flow.
You could also use some small FET's, each as a switch, which allows current to flow both ways. These can then be controlled by a decade counter (4017B?), which is incremented via a push switch (effectively, acting like a rotary switch, with one push button sequentially seletecting each fet). This could also give you the LED's, since the output from the decade counter could drive both the FET and an LED. It really depends on cost, size, and complexity of the circuit you want.
Of course, you would need two of these circuits, since there are two 'rotary switches' needed. I would say, give the multiplexer/demultiplexer thing a go, it'll be less complicated, but may not work. If you have already build the frequency counter circuit, check which are the inputs and which are outputs to and from the rotary switches, using diodes.
If you are struggling, then I could draw up a quick dirty schem to show you exactly what I mean.
Good Luck,
BuriedCode.