I have heard that you can sub oil, but I have never tried it. Eggs make the cake lighter, so if you have 2 large or extra large eggs, you may have enough. I would say try it before you sub anything, and if it doesnt work, run out and buy more eggs tomorrow. If it does work, well, then you know! 
Do you have meringue powder? That is egg...add a tablespoon, if not add a tablespoon of mayo...it is mostly egg too...
This is a culinary school tip...and yup it works! Although, I would not use all mayo in place of eggs, you can, it just is a bit more crumbly...have done it for a good tasting product, yet a different texture when using all the mayo in place of eggs, but with the ratio above the mayo will work fine, and the meringue powder always works...
iv had that problem too and i just baked mine with 2 eggs and it was fine i have always thought that the eggs were mostly to make your cake more firm.
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