Yes you can have a private method in webservices but you will use it only within webservice's class,you will not be able to call it from outside the webservice at all
Example:
[WebMethod]
public static string WebMethod(string postCode)
{
// My webmethod code
string str = Add(2,5);
}
private static string Add(int a, int b)
{
// My private method code
}