I need to make a 6' round for one of my daycare kids for father's day, (as the kids gift to dad)... I only have 2 eggs... I use a box mix that calls for 3 eggs, I usually put 4...

can I add more oil to make it stick together?

Any of the following will do the job: oil, water, applesauce, sour cream, yogurt, corn syrup, maple syrup, jam, booze...you name it.

There is a Chocolate Mayonnaise case recipe out there that replaces oil and eggs with Mayonnaise, you might check that out.

I have made ALL of my cakes using just 2 whole eggs per mix Don't need anything different.
IF you just can't live w/that then a couple of tablespoons apple sause will help.