
Carnegie Libraries of Vermont
One especially nice reference for these libraries is In This State: Celebrating Vermont's Carnegie Libraries.
Completed with the discovery that the Morristown Centennial Library is in Morrisville.
Bellows Falls (Rockingham Free Library)
And this H.M. Francis & Son building is what we have today, with a few additions. Eventually, according to Wikipedia, the powers that be finally accepted Andrew Carnegie's money in 1908.
This building is still in use.
Newvochrome postcard, mailed in 1911. Its caption places the Library in Bellows Falls, as does the Library's web site. Technically, it's in the Town of Rockingham.

Burlington (Carnegie Fletcher Library)

Published by Chas. W. Hughes, Mechanicsville, N.Y.
Curiously, the Library's history page makes no mention of the architects or builders of this 1904 Carnegie-funded library building. Perhaps it's because the darn thing nearly fell down in 1973. It took until 1977 to save the building, and an addition was dedicated in January, 1981.
Fair Haven
1905 Carnegie grant.No web site, but there is some information, including a picture that shows the library still in use. The Library also had a 1997 addition.

(L) Ah, the wonders of autumn in Vermont! The leaves cover the ground in a cozy blanket, and the retoucher restored them to the trees.
(R) Some mighty tropical looking plants decorate the library's lawn.
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Morrisville (Morristown Centennial Library)

(L) Photo postcard, never mailed.
(R) A.L. Chenoy monochrome postcard without a date in the cancellation.

I'm somewhat unclear as to the distinction between Morristown and Morrisville, but the Library's home page calls it the Morristown Centennial Library. The photo looks like these images. I'll accept that this has completed my collection of Vermont Carnegie Library postcards.
1911 grant: still in use.