No, there is no such web site. You just have to ask them. While HIPPA rules limit the information doctors can give out on other patients, some do have patients who have volunteered to be references. You could ask if they have any. Also, I find people often just ask their Gp's for a referral. What you should actually ask is who they would send their wife/child/mother/etc to. There is a difference. And don't forget to check online for lawsuits, sanctions by the local/state AMA, etc. There are lots of web sites that can give you that information.
Also, if your child has a particular disease/condition, there is most likely a support agency for that - like American Cancer Society, MS society, etc. Those groups often have lists of approved/recommended docs.
Good luck!