You can give them a teething ring. Many teething rings can be chilled in the refrigerator which can soothe the pain of cutting teeth. Allowing your baby to chew on something will help to break down the gum which will help the teeth to emerge. Many babies also like to chew on wet, chilled wash clothes, or have their gums rubbed with the pad of a finger. You can get pads to put over your finger.

You can give your child a small dose of an infant’s pain reliever to help relieve discomfort. If your child seems to be very bothered by teething pain, you can apply a small amount of numbing medication to the inflamed gum area. However, be cautious. Too much of this topical treatment can numb a baby’s entire mouth and produce swallowing problems.
Good for you for not wanting to do this. The old time remedy is a little vanilla.

It is important that you keep your baby’s gums clean and healthy. You should clean your child’s gums with a warm cloth-- even before a tooth appears. This should be done after feedings and at bedtime. Once your baby has their first tooth, you should brush it with a small, soft toothbrush when you are cleaning their gums. It is important to understand that the health of baby teeth (or primary teeth) is just as important to maintain as permanent teeth. Baby teeth help to make way for permanent teeth, and they also help muscles and the jawbone to develop properly. (You have to expect this in my answer.)

Keep in mind that teething never causes illness. If your baby has a rash, fever, or other symptoms of illness, you should take them to the pediatrician. Histological studies show no pain from teething. That is no comfort to mothers, who know better.