Penguin makes an excellent cornbread mix that I make without dairy or eggs. It has a great taste and bits of corn kernels in the mix. My kids eat them by the handfulls; they are good bribes for eating the other items on their plates.
I make it without eggs or dairy by using soy milk and substituting 1 teaspoon baking powder + 1 Tablespoon water + 1 Tablespoon vinegar (added last) for each egg. If possible, let the mixture sit for a few minutes before you pour it into the muffin cups. Cook 18 minutes for muffins.
The only drawback to not using eggs is that they are a bit more crumbly, but they taste great. You can use vanilla soymilk for a sweeter taste.
You can buy a big box at Costco that contains several packets that make a dozen muffins or one loaf each. Occasionally they are out of stock, so I buy a couple of boxes at a time.