Hi. Yes. You could use an oscillator, a counter and some logic, e.g. a 555, a 4017, a bunch of diodes and resistors, a octal buffer and two 7447 to drive the two 7-segment displays
For showing the exact number sequence in post #1 I think the only practical solution is to use a micro. It would be possible, but far more complex, to do it with discrete logic ICs. Not sure where a JK flip-flop would fit into the scheme of things.
I agree that a microprocessor would be the easiest. A simpler way with descrete IC's would be to use two CD4543 decoder drivers, a 4017 counter to divide by 6 and a 555 as a clock oscillator, and some diodes to select the abcd inputs of the 4543 decoder drivers. KYtan where are you at, in the world?. I have all the parts available that I described, and I would be happy to help you design the system and if possible perhaps send you the parts.
I do have two segement LED's also.
Here is the basic design of the circuit less the counter and clock for one digit. By connecting diodes to the inputs of the 7446 the desired number will be shown on the LED display. You could use some JK F/f but I think it would take four of them arranged in a johnson counter, the you would have to decode it.
I construct the circuit as shown in attachment below. However, the reset part when reset, it suppose to be "00" but it shows "02". I try to change to the Nor gate to or gate(it did solve the reset problem) but the 1st number as shown post number 1 cant appear and a "0" is shown. Anyone know how to solve it?