"No, thank you."
Danke is a Dative verb (http://german.about.com/library/verbs/blverb_dativ.htm) which makes the following pronoun a dative one, Ihnen (Capital letter) is the dative form of Sie. I think :)
"Nein, danke" is the common phrase. "Nein, danke dir." This can get a individual note. But in general it is better to say: "Nein, ich danke dir" or "nein, dankeschön."
"Nein, danke Ihnen" and "nein, danke euch" sounds a little bit odd. "Nein, ich danke Ihnen (or euch) is correct. But one could say: "Nein, danke euch beiden" (or "euch dreien" or "euch allen").