You need something ready-made or a kit, so I looked around and am wondering if you need it to reset from 59 back to 0 automatically. If not, what happens when it gets to 60?
Here is one kit that you might consider. You would have to cover up the hours digits:
**broken link removed** and scroll down to kit FK435.
Another approach is to get a counter kit, like this one:
**broken link removed**
and add a 1 hz pulse circuit to the input.
Another way to do it is to get a small microprocessor development board, like maybe this one:
SparkFun Electronics - 18 Pin PIC Development Board
and then wire in one of these circuits on to that board:
and then write a simple program that counts up on the displays at exactly 1 second per count. If this level of programming is too complicated, perhaps someone here could do it, or you might find a local technical school student who could do it. It is not a complex program to do. Nigel has a do-it-yourself PIC board that connects to the 7 segment LED board and he shows you how to wire it. It all starts here:
For your purposes, you will need to go through the first couple of tutorials and then go to tutorial 10. Or you can find an electronics student to do this for you at the local college, that might be easier and faster.