UPDATE: This was originally posted June 18, 2020:

April 1954, Dane County, North Carolina: https://digital.ncdcr.gov/digital/collection/p249901coll36/id/336. The jeep was painted green.

March 1950, Dane County, North Carolina: https://digital.ncdcr.gov/digital/collection/p249901coll36/id/331
An April 15, 1948, newspaper article in the Winona Republican (Winona, Minnesota) claimed that there were roughly 377 bookmobiles traveling the United States, out of which only one was a jeep.
Two years later, by 1950, the jeep was proving more popular for use as a bookmobile, because it could access rural areas more easily than other vehicles. I doubt there are any records on how many jeeps were used as bookmobiles, but at least one appeared in multiple photos and articles: The Dare County Jeep Bookmobile.
Dare County purchased it’s first jeep in 1950, hence all the photos and news articles on this post. According to the library’s history page: “After the war, the library continued to grow. In 1950, the first bookmobile was purchased – a green Willys Jeep converted for this purpose began making regularly scheduled runs. As there were then no bridges from the mainland or to the Outer Banks, all trips involved ferries. Georgia Harwood retired in 1956, succeeded by Jean Turner Ward, who served as librarian for the next fifteen years.”
This full page article with photos was published in North Carolina’s News and Observer on April 23, 1950. It appears the new jeep bookmobile had just been put into service.
This next article, which predates the above article by 13 days, was published in North Carolina’s News and Observer on April 23, 1950.
Dare County’s digital archives provided additional photos: