A birder named Gregory Harber writes on BirdChat this morning "thata since Pileated is derived from the Latin word, Pileum, one needs to look at the Latin pronunciation, where the "i" is a "long i." The "long i" in Latin sounds like the "i" in "machine," which of course is an "e" sound. So technically it is not Pie-lee-ated or Pill-e-ated. It is i Pee-le-ated. (He makes reference to Sister Aiden, which suggests a nun, which suggests lessons learned well).
One again, according to "The Audubon Society Encyclopedia of North American Birds" by John K. Terres, Parula is pronounced "PARR-you-la". The word represents the blue hue found on the bird. – Dave DeReamus
DeReamus also wrote: “Actually, Terres mentions that also. For "Northern Parula," he writes: "Parula americana (PAR-you-lah ah-mer-ih-CANE-ah); genus name: from Lat. parula, dim. of parus, titmouse; little titmouse."
"Parulid," Terres writes: "(PARR-you-lid). A popular collective name for any bird of the Warbler---American Wood Warbler Family."
And, for "Parula (PARR-you-la) blue,” he writes: "A color, blue in hue, of low saturation and medium brilliance. The Northern Parula warbler is a small grayish-blue bird of the American Wood Warbler Family."
So, DeReamus writes, the accent is consistently on the first syllable and not the middle one.
All of this is taken from email on the BirdChat network. This discussion began when someone asked for the correct pronunciation of “scaup,” a duck species. I won’t get into that. However, Arthur A. Allen's pronunciation on the old Peterson Field Guide to Bird Songs, was "Skawp". Allen is a historic figure in American ornithology. I suspect most of us don't care. Seeing bird is the challenge.