WT literature was still using B.C./A.D. at least until the year 1958, instead of B.C.E./C.E. For example see the following.
Page 199 of Rutherford's book called "Enemies" (copyright 1937) says "year 1848 (A.D.)". For another example, see Rutherford's book called "Religion", copyright 1940. Page 336 of that book says "In the year 1914 (A.D.) Christ Jesus, the King, was enthroned." The WT book called "Theocratic Aid to Kingdom Publishers" (copyright 1945) says A.D. twice on page 326 and four times on page 327. The WT book called ' "Equipped for Every Good Work" ' (copyright 1946) says B.C. and A.D. multiple times. The WT book called "What Has Religion Done for Mankind? (copyright 1951) on page 299 says "607 B.C." and "A.D. 1914". The WT book called "Qualified to be Ministers (the edition copyright 1955) says B.C. twice on page 126 and it says A.D. on page 290. The WT book called "From Paradise Lost to Paradise Regained" (copyright 1958) on page 102 says "In 620 B.C. ..." and page 130 says "in the autumn of A.D. 29 ...." The NWT revision of 1961 (Second Printing) on the title page says
"--Revised A. D. 1961--'. Page 1459 says B.C.E. and page1460 say "B.C.E.
and A.D." It surprising that while that Bible edition says B.C.E., it says A.D. instead of C.E. The page in the back of the 1961 NWT which lists the availability of the 5 Hebrew Scriptures volumes and the Christian Greek Scriptures volumes also say A.D. in reference to the release date of each of those volumes; and volume 5 of the Hebrew volumes was released in 1960.
Note in the above examples, uses of B.C. and A.D. might be on other pages besides the ones I mentioned above, I merely scanned the books quickly to see a usage of B.C./A.D. versus B.C.E./C.E.
In contrast the pocket size edition of the the WT book called ' "Things in Which it is Impossible for God to Lie" ' (copyright 1965) says on the bottom of page 3 the following: 'DATING: In dating, the abbreviation B.C.E. stands for "Before Our Common Era," and C.E. stands for "Of Our Common Era." ...." B.C.E. and A.D. appear also on other pages of that book. Likewise the First Edition (pocket size edition) of the WT's "Life Everlasting in Freedom of the Sons of God" book (copyright 1966) has the same message about dating as the book from 1965.
Thus it seems that the WT literature didn't begin saying B.C.E./C.E. until around the years 1961 - 1965. I never found any reason stated in the WT for why they switched to the other terminology. But I have a guess as to why.
When the B.C./A.D. system was created it was based upon the belief that Jesus was born on Dec. 25th of the year 1 B.C. and thus that the first year of his human life ended in A.D. 1 (A.D. meaning "in the year of the Lord" in Latin), see https://en.wikipedia.org/wiki/Anno_Domini. But modern scholars believe that Jesus was born before the year 1 B.C. (see https://en.wikipedia.org/wiki/Date_of_birth_of_Jesus which says that most theologians and most scholars "accept a date of birth between 6 and 4 BC" for Jesus), and the WT also says that Jesus was born before the year 1 B.C. The WT's book called "Aid to Bible Understanding" - "1971 Edition" says on page 920 in the article called "Jesus Christ" that "Jesus evidently was born in the month of Ethanim (September-October) of the year 2 B.C.E. ...." Page 56 of Vol. 2 of the Insight book says that also.
Thus, it is a misnomer to use the terms B.C. and A.D. if you believe
Jesus was born prior to the year 1 B.C. Saying Jesus Christ was born in the year 2 B.C. is literally saying "Jesus Christ was born in the year 2 Before Christ" - a contradiction. I think that is the likely reason
why the WT switched to the newer terminology. It fits with their claim of
abandoning false doctrines/teachings and false practices (especially those of what the WT labels as Christendom).