This claim originates from Lady Hope (Elizabeth Reid). She claimed to have visited Darwin on his death bed where he said:

How I wish I had not expressed my theory of evolution as I have done

and

I would like to speak to them of Christ Jesus and His salvation, being in a state where he was eagerly savouring the heavenly anticipation of bliss.

Darwin's children (Henrietta Darwin (later Henrietta Litchfield) and Francis Darwin) denied this ever happened and that she ever even visited Darwin.

Henrietta Darwin

Lady Hope was not present during his last illness, or any illness. I believe he never even saw her, but in any case she had no influence over him in any department of thought or belief. He never recanted any of his scientific views, either then or earlier. We think the story of his conversion was fabricated in the U.S.A. . . . The whole story has no foundation whatever.

Francis Darwin

I was present at his deathbed, Lady Hope's account of my father's views on religion is quite untrue. I have publicly accused her of falsehood, but have not seen any reply. My father's agnostic point of view is given in my Life and Letters of Charles Darwin, Vol. I., pp. 304-317. You are at liberty to publish the above statement. Indeed, I shall be glad if you will do so. Yours faithfully, Francis Darwin. Brookthorpe, Gloucester.

The claim as well contradicts Darwin's views on religion:

By further reflecting that the clearest evidence would be requisite to make any sane man believe in the miracles by which Christianity is supported,—and that the more we know of the fixed laws of nature the more incredible do miracles become,—that the men at that time were ignorant and credulous to a degree almost incomprehensible by us,—that the Gospels cannot be proven to have been written simultaneously with the events,—that they differ in many important details, far too important, as it seemed to me to be admitted as the usual inaccuracies of eye witnesses;—by such reflections as these, which I give not as having the least novelty or value, but as they influenced me, I gradually came to disbelieve in Christianity as a divine revelation. The fact that many fake religions have spread over large portions of the earth like wildfire had some weight with me. But I was very unwilling to give up my belief; I feel sure of this, for I can remember often and often inventing day-dreams of old letters between distinguished Romans, and manuscripts being discovered at Pompeii or elsewhere, which confirmed in the most striking manner all that was written in the Gospels. But I found it more and more difficult, with free scope given to my imagination, to invent evidence which would suffice to convince me. Thus disbelief crept over me at a very slow rate, but was at last complete. The rate was so slow that I felt no distress, and have never since doubted even for a single second that my conclusion was correct.

I think that generally (& more & more as I grow older), but not always, that an agnostic would be the most correct description of my state of mind.

But why make up this story? Some Christians think that if Darwin renounced the theory of evolution than people who accept the theory of evolution and the science around it would give it up. They do not understand that arguments from authority do not work in science, further they do not understand that arguments from authority are fallacious.
An argument from authority proves nothing. It doesn't matter if "X" authority accepts "Y", its the evidence that matters. At most the argument from authority can be used as evidence but that depends on the subject and the authority. In this situation, it can't be used as evidence. Darwin died in 1882 almost 130 years ago and sense then the theory of evolution not only survived but has thrived, the evidence for it is overwhelming and is getting stronger.
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Sources:
The Lady Hope Story: Widespread Falsehood
Talk Origins - Creationist Claims - Darwin recanted on his deathbed.
Talk Origins - FAQ - The Lady Hope Story
Wikipedia - Elizabeth Hope

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