Start from basics - in 555 timer you set timing normally by varying a pot and start timing by a low going pulse to the trigger pin.

So in your 89cx051 how would you want to set the timing ? - thumbwheel switches/keypad/selector switches ?
And how would you start the timing - a pushbutton ?

You will have to use one of the timers ( preferably Timer 2)to genererate an interrupt once every 50mS and then from this derive the 1 Sec event and from that derive the 60 Sec event. That will be the code mostly - rest is to just compare what the user wants and stop at that point of time...

And more important - will you code in C or Assembly ?

Raghu