Unwin 2006 used a node-based definition anchored on Preondactylus, the most basal form in his phylogeny. But any node-based definition like this will end up looking extremely arbitrary as soon as the inevitably more primitive forms come to light. Branch-based would be just as bad, inevitably including everything down to (presumably) basal ornithodirans nowhere near a gliding, let alone flying, stage. Plus, we've already got Pterosauromorpha, which is a nice compliment to Dinosauromorpha if they're really sister groups. We're forced to either exclude a big chunk of 'classic' pterosaurs or include a big chunk of very un-pterosaurian taxa. There isn't even a pterosaurian Archaeopteryx with the historical clout to serve as a good arbitrary specifier. It would be like having to define Aves if there were no crown birds and the most primitive fossil bird known was Ichthyornis.
The only fair and arbitrary thing to do, off the top of my head, would be to pick the first two described taxa and use those as specifiers (Pterodactylus + Rhamphorhynchus). This would render Dimorphodon, Eudimorphodon, etc non-pterosaurs, but there are going to be some very Eudimorphodon-like non-pterosaurs either way. Alternately, use whichever pterosaurian taxa were originally included when Pterosauria was coined. Which would be Pterodactylus + Rhamphorhynchus + Dimorphodon (and maybe a few others initially included in Pterodactylus?).
The only way to retain the classic winged lizards sense is to use an apo-clade, but this might not be ideal for Pterosauria itself. We could always resurrect some oldies like Ornithosauria or even von Meyer's Pterodactyli (or is that name unavailable due to the supposed emendation to Pterodactylidae?).
How about "Pterodactyles"?
