Someone is trying to take me to court for a supposedly verbal agreement.

You don't say specifically, but I gather that you are the grandparent in this situation, and your daughter is the parent.  If you are not the parent or legal guardian of the child, you would normally not be liable for expenses relating to your granddaughter absent a contract in which you agree to be bound.  Your former daycare provider claims to have such an oral agreement with you; you claim she doesn't.  While some types of contracts are required to be in writing, most are not.  One type of contract which generally is required to be in writing is a contract to be responsible for the debts of another, so if the daycare worker is claiming that you agreed to guarantee your daughter's obligations to pay the daycare worker, an oral agreement probably wouldn't stand up.  If she is just claiming a straight agreement where you agreed to pay for her services, however, such an agreement can be oral.  If you had a written contract with her, that would probably preclude her trying to claim a written agreement, but as it stands, and without knowing any of the evidence that either of you will present, there is no guarantee that a judge or jury will not believe her.