I originally asked this on Christianity.SE and later it was moved to Mythology.SE, but it remains unanswered.
It is actually very easy to find a citation for the quotation's source, the problem is that the commonly published attribution is wrong.
Searching for "evergreen tree which sprang out of a dead tree stump" gets nearly 3000 hits.
The Seed of the Woman and the Power of Darkness - Donbor Syiemlieh - Google Books provides an example:
"An old Babylonish fable told of an evergreen tree which sprang out of a dead tree stump. The old stump symbolized the dead Nimrod, the new evergreen tree symbolized that Nimrod had come to life again in Tammuz! Among the Druids the oak was sacred, among the Egyptians it was the palm, and in Rome it was the fir, which was decorated with red berries during the Saturnalia!" (Walsh, Curiosities of Popular Customs, p. 242).
Obviously I didn't check all results, but those that I did check contain that same quotation, and almost all give the same attribution.
The problem is, while page 242 of that book does talk about Christmas trees, and the writing style is similar, it doesn't include the above quotation or anything like it:
The quotation doesn't appear elsewhere in that section or anywhere else in the book.
So what is its origin?