Need a design – Simple one button push button to turn on 4 different LED (3mm Dome) every time you press the button.
Attached is a circuit file that might work for you. Or make it simpler combining it with the circuit shown below.
555 Oscillator and Running Lights
Make a monostable with 555 as shown here – 555 Timer based Circuits – and output it to a 4017 with above info, i am sure you can build or design what you want.