What sort of first aid certificate should I do for babysitting?

Red Cross or 4H. Most local red cross chapters and many 4h chaapters run regular baby-sitting training courses. Certification would demonstrate that you take the job seriously & will know how to avoid pitfalls as well as responsibly take care of any problems which might arise. More importantly, the child will be safer and you will have gained more self confidence. Good luck.
First aid. You probably need to get certified in cpr, which is offered at local hospital, fire department, or large medical clinics.
Heartsaver. There are several options when taking first aid and CPR classes. For babysitting, you can take the american heart association's heartsaver pediatric first aid as this would satisfy your request. However, many parents will want to know that you also are CPR certified, in which case you should also take the heartsaver cpr/aed, which will train you for infant, child and adult CPR and aed.