There is no counter IC, the mux is a data select and your inputs are floating, you have to demux it to drive encoder then decoder driver for display. Well you don't have to demux it most of the time.
I will look into some. What is wrong with using a ripple counter or a cascading counter???
For mux displays:
2) 74192 counters, 1's counter and decade counter
1) 555 Timer
1) 74157 to 7447 decoder driver
1) free running clock, pulse, logic switch, etc (another 555 astable pulse can be used here)
All the inputs are used on the mux. I didn't use any transistors on my project display.