Darwin died on April 19, 1882, at the age of 73 and all the evidence says, "no", he did not make a deathbed conversion nor did he renounce evolution. This has been verified by Darwin's family, who have written a variety of articles on this very subject shortly after his death.
The story was believed to have been fabricated by Elizabeth Reid Cotton who claimed to have made several death bed visits where she experienced Darwins confession. However, at best, it was concluded that her visits were always under the watchful eye of a family member. It was later determined Ms. Cotton was a deeply religious woman who was troubled by Darwin's naturalistic ideas of which may have influenced her to fabricate such a story.