I can add an attribute to items in a RadioButtonList item like so:
PaymentMethodDropDownList.Items[0].Attributes.Add("onclick", "javascript:showNoMethods();");
PaymentMethodDropDownList.Items[1].Attributes.Add("onclick", "javascript:showCreditCardMethod();");
PaymentMethodDropDownList.Items[2].Attributes.Add("onclick", "javascript:showSendPaymentMethod();");
However, when I try to add the attributes to a DropDownList control it doesn't seem to work. I would expect it to be similar.