[AutumnBison (OP)]

Have there been molecular (not fossil) evidence of when the following bird orders debuted?

Coraciiformes (bee-eaters, rollers, kingfishers, todies and motmots)
Piciformes (woodpeckers, toucans, jacamars, puffbirds and barbets)
Psittaciformes (parrots)

I ask this because of two reasons.  One, because the first two orders are featured in the Speculative Dinosaur Project, a speculative evolution scenario which detailed on how life might've looked had the dinosaur empire not fallen 66 million years ago.  This would have suggested that both clades were in our timeline around long enough to witness the Chicxulub extinction event, but is this true? 

Two, the Wikipedia article on "Parrot" states that the order debuted 50 million years ago in the Eocene, yet the molecular evidence suggests that Psittaciformes is a much older order than that:

   

Molecular studies suggest that parrots evolved approximately 59 million years ago (Mya) (range 66–51 Mya) in Gondwana. The three major clades of Neotropical parrots originated about 50 Mya (range 57–41 Mya).[6]

But the article on "New Zealand parrot" says this:

   

The superfamily diverged from the other parrots around 82 million years ago when New Zealand broke off from Gondwana, while the ancestors of the genera Nestor and Strigops diverged from each other between 60 and 80 million years ago.

Which article is more accurate?