Please find attached a part solution to your problem. It's certainly not the most economical of solutions, but it will work. The solution in my attachment is only for the required LED pattern - you still need to come up with a suitable clock system for it all, and you need a way of stopping the clock once A and B both = logic 1. When your push button is pressed the 2-bit counter needs to be reset, and the clock should be allowed to start again until A and B = logic 1, when it should stop. This process is then repeated over and over as many times as you push the button!
Please be aware that the push button in my circuit is NOT supposed to represent the push button in your description of the problem - I used it to simulate a clock so that I could test the LED pattern in multisim. It should be emitted from your design (assuming you use this one) and replaced with your clock / latch system.
Brian
----- edit -----
The website didn't accept my attachment because it was above 19KB!!!! Give me your email, I'll send the Word document with the circuit in it to you.