The fastest way to get an egg is if the two Pokemon are of the same species and have the same ID number.

Same species, different ID numbers

The chance of getting an Egg is 69.3% (has a value of 70). The Day-Care Man will say: "The two seem to get along very well."

The fastest way of getting an egg with different species is if they have the same ID number.

Different species, different ID numbers

The chance of getting an Egg is 49.5% (has a value of 50). The Day-Care Man will say: "The two seem to get along."

This chance is raised to 79.5% when wielding an Oval Charm (has a value of 80).

So just put those combinations in the day care center for the fastest results.

**Here** is the list of *all* the possible combinations and the percentage of getting an egg.

**Source**

Hope I helped!