Ironically, both have been proposed by very prominent atheists.
1. God can cause specific mutations (Richard Dawkins). The background of "random" mutations is so high that if God directs a specific cosmic ray to a specific nucleotide or interferes with gene duplication, etc. we cannot detect that.
2. A bit of artificial selection (Daniel Dennet). If God engages in a bit of artificial selection to weed out variations He does not want, we cannot read the fossil record fine enough to detect that.
"Darwinism is widely misunderstood as a theory of pure chance. Mustn't it have done something to provoke this canard? Well, yes, there is something behind the misunderstood rumour, a feeble basis to the distortion. One stage in the Darwinian process is indeed a chance process -- mutation. Mutation is the process by which fresh genetic variation is offered up for selection and it usually described as random. But Darwinians make the fuss that they do about the "randomness" of mutation only in order to contrast it to the non-randomness of selection, the other side of the process. It is not necessary that mutation should be random in order for natural selection to work. Selection can still do its work whether mutation is directed or not. Emphasizing that mutation can be random is our way of calling attention to the crucial fact that, by contrast, selection is sublimely and quintessentially non-random. It is ironic that this emphasis on the contrast between mutation and the non-randomness of selection has led people to think that the whole theory is a theory of chance. ...
One could imagine a theoretical world in which mutations were biased toward improvement. Mutations in this hypothetical world would be non-random not just in the sense that mutations induced by X-rays are non-random: these hypothetical mutations would be systematically biased to keep one jump ahead of selection and anticipate the needs of the organism ...
Darwinians wouldn't mind if such providential mutations were provided. It wouldn't undermine Darwinism, though it would put paid to its claims for exclusivity: a tailwind on a transatlantic flight can speed up your arrival in an agreeable way, and this doesn't undermine your belief that the primary force that got you home is the jet engine." R Dawkins, Climbing Mt. Improbable, pp 80- 82.
Dennett, from Darwin's Dangerous Idea, pp. 317-318 "Indeed, all the biologists I have queried on this point have agreed with me that there are no sure marks of natural, as opposed to artificial, selection. In chapter 5, we traded in the concept of strict biological possibility and impossibility for a graded notion of biological probability, but even in its terms, it is not clear how one could grade organisms as 'probably' or 'very probably' or 'extremely probably' the products of artificial selection...It would be foolhardy, however, for any defender of neo-Darwinism to claim that contemporary evolution theory gives one the power to read history so finely from present data as to rule out the earlier historical presence of rational designers -- a wildly implausible fantasy, but a possibility after all."