Hi,
I have done a quick schematic for your circuit needs, it may not be what you were looking for 'though, I hope it is a good start anyway. Get a second opinion in case I've made any glaring mistakes.
The components that do not have values stated are because without knowing the voltages it can't be calculated. The components that do have values, assuming you use... let's say from 5 - 12V for the analog circuit, should all be fairly correct, but as ever with a circuit, you may and most likely will need to play around with some of the resistor values a little to fine-tune it all.
I have also assumed that your relays are indicator relays.
This circuit could quite likely be done with the transistors, a 4017 and a flip-flop IC like the 4013, but I've never used one so wouldn't like to invent an untried circuit, maybe some-one else here could advise how to do that, as it would save using two 555s.
The capacitor on the input of the 555s is to make it trigger correctly, otherwise the circuit won't work as the timer needs the trigger signal to go high again in a specified time to function correctly. The resistor and capacitor connected to the 4017 reset pin make it always start on the first output when it is powered up, the resistor is there as that isn't an output. In theory, and it should be so in practice, press once (allow a few milliseconds between presses or it won't respond) and a timer triggers a relay for very roughly 30 seconds, press the button twice and it will move to the next 4017 position and trigger the second timer/relay, press a third time and it will reset to the first "do nothing" position.
It's not ideal, as you need to cycle through the two relays to reset it, and I really suspect this is better accomplished using an up/down counter IC or better yet a PIC or similar. Analog is great, but can become unwieldly just to operate a "simple" logical sequence which needs to follow several options with only one user input...
Anyway, hope it is of some use, at least.