As another said, Dungeon issue 110, page 63, has a tiny sidebar saying that full stats for a dragon-king would only be useful to the few DMs that would actually have their PCs fight one..... So in other words Paizo's team didn't feel like bothering to stat up a dragon-king, and left it up to us poor DMs to cobble together ourselves.
The sidebar only says that if you need it on the fly, treat a dragon-king as having the physical characteristics of a great wyrm (no particular dragon type, so I guess just choose one), the spellcasting ability of a 22nd-level wizard (with epic spells too as appropriate, one of which would be the epic-level ritual spell that made them into a dragon-king), and the psionic manifesting ability of a 22nd-level psion (including epic powers).
Yeah, as if that's helpful advice. -_- Not like it wouldn't take forever to stat up a great wyrm epic wizard epic psion..... -_-