JOEL - We all know that the three witness eventually either left or were excommunicated from the church for various reasons. But there are plenty of records supporting the fact that they never denied their testimony of the Book of Mormon.
The Times and Seasons reference is not any kind of official statement by church leaders but simply a poem written by J. H. Johnson:

"Or prove that Christ was not the Lord
Because Peter cursed and swore?
Or Book of Mormon not his word
Because denied, by Oliver?
Or prove, that Joseph Smith is false
Because apostates say tis so?"

J. H. Johnson never had an opportunity to witness any denial made by Oliver Cowdery. He was in Kirtland at the time of Cowdery’s excommunication in Missouri and after that had no known contact with him. (Matthew Roper (1993), “Comments on the Book of Mormon Witnesses” Journal of Book of Mormon Studies (Provo: FARMS) 2:2, p. 172.) So even if the line in the poem about Oliver was meant to infer disbelief in the Book of Mormon, Johnson may have been simply repeating an unsubstantiated rumor.
There are no other documents that indicate that Oliver ever denied his testimony of the Book of Mormon. There are several to the contrary however. According to David Whitmer in his article "An Address To all Believers in Christ":
"It is recorded in the American Cyclopedia and the Encyclopedia Britannica, that I, David Whitmer, have denied my testimony as one of the three witnesses to the divinity of the Book of Mormon; and that the other two witnesses, Oliver Cowdery and Martin Harris, denied their testimony to that Book. I will say once more to all mankind, that I have never at any time denied that testimony or any part thereof. I also testify to the world, that neither Oliver Cowdery or Martin Harris ever at any time denied their testimony. They both died reaffirming the truth of the divine authenticity of the Book of Mormon. I was present at the death bed of Oliver Cowdery, and his last words were, "Brother David, be true to your testimony to the Book of Mormon.'' He died here in Richmond, Mo., on March 3d, 1850. Many witnesses yet live in Richmond, who will testify to the truth of these facts, as well as to the good character of Oliver Cowdery."(Chapter 1)
A few other problems with the Cowen statement is that Oliver did not serve as the secretary for the Methodist Church. According to biographer Phillip R. Legg, Oliver Cowdery served as secretary of a Presbyterian school called the "Western Reserve Teacher's Seminary and Kirtland Institute", where he also taught some of the classes. ("Oliver Cowdery, The Elusive Second Elder of the Restoration", 1989)
Oliver did join with the Methodists for a time, but eventually he left Ohio and returned to Iowa where his wife and daughter reunited with the Mormon Church. Before he was baptized he bore his testimony to the congregation of the church which had gathered for a conference:
“I wrote, with my own pen, the entire Book of Mormon (save a few pages) as it fell from the lips of the Prophet Joseph, as he translated it by the gift and power of God, by the means of the Urim and Thummim, or as it is called by the book, Holy Interpreters. I beheld with my eyes, and handled with my hands, the gold plates from which it was transcribed. I also saw with my eyes and handled with my hands the Holy Interpreters. That book is true. ...It contains the everlasting gospel, and came forth to the children of men in fulfillment of the revelations of John, where he says he saw an angel come with the everlasting gospel to preach to every nation, kindred, tongue and people. It contains principles of salvation; and if you, my hearers, will walk by its light and obey its precepts, you will be saved with an everlasting salvation in the kingdom of God on high.” (Andrew Jenson, LDS Biographical Encyclopedia, [SLC: Andrew Jenson History Co., 1901 1:246)

On the day he died Lucy P. Young, his half-sister, was at his bedside and reported:
“Oliver Cowdery just before breathing his last, asked his attendants to raise him up in bed that he might talk to the family and his friends, who were present. He then told them to live according to the teachings contained in the Book of Mormon, and promised them, if they would do this, that they would meet him in heaven. He then said, ‘Lay me down and let me fall asleep.’ A few moments later he died without a struggle."(Jenson, 1:246)