I don’t think, you need to know the duration, but rather, which enzymes are transcribed at that phases

JackBean is absolutely right. For your purpose you don’t need to know the duration of any cell cycle phase. The cell cycle is a very complex network of lots of proteins, however major players are cyclin-dependent kinases (CDKs). These enzymes (in budding yeast there is actually only one, propably also in the fission yeast S.pombe) are regulated by cyclins (http://en.wikipedia.org/wiki/Cyclin). Different cyclin variants are only expressed during different cell cycle phases to enable the activation of the respective CDK (or determine a specific activity if there is only one CDK).
So to let cells shine in a specific phase of the cell cycle a good approach would be to make fusion constructs of a fluorescent protein and the different cyclins. If you have enough distinguishable reporters in yeast you can even put them all into one cell. By only using GFP you need of course to seperate the transformation events. Good luck for your competition!