In “his general talk on the evidence for evolution,” Jerry Coyne says he gives “a list of seven observations that, if repeated and confirmed, would disprove parts of the theory of evolution.” This would show “that it is a scientific theory in the Popperian sense of being falsifiable.”
I think we should congratulate Coyne for accepting a Popperian test for judging the scientific status of evolutionary theory. It is notoriously easy to circumvent the falsification test and for this reason it is today rarely used as a way of deciding whether a theory is scientific or not. But it is always good to see someone try. Especially as dogmatic a Darwinian as Jerry Coyne.
Coyne follows with his Point 1: the “fossil mammals in the pre-Cambrian” argument, first (supposedly) brought up by J.B.S. Haldane, and then definitely by Richard Dawkins more recently. Such a discovery, said Dawkins, would “completely blow evolution out of the water.”
That claim has been ably met by ENV, referring us to articles on the subject by Paul Nelson that appeared here in January 2010. In what follows I shall respond to Coyne’s Point 2. He writes that evolution would be disproved by:

• Adaptations in one species good only for a second species. There are plenty of adaptations in species that are good for other species, but also help members of the first species: these are the basis of mutualisms. (Cleaner fish, for example, remove parasites and dead tissue from other marine fish, but thereby gain a meal.) But we don’t expect to see — and don’t see — adaptations in one species that evolved solely for the benefit of another species.

In other words, he is expecting us to find an “adaptation” (in the example he gives, “adaptation” means a form of behavior) that is certainly and provably unhelpful to those exhibiting the behavior. This we “don’t see,” says Coyne.
The reason we don’t see it, of course, is that it is notoriously easy to concoct a “Just So” story explaining why X’s behavior can be construed as useful to X. An example of a possibly self-harmful adaptation is the warning cry of a bird who thereby alerts the neighborhood to the presence of a predator. But such cries may also reveal the whereabouts and presence of the crier. It could therefore be construed as “solely benefiting another species.”
Is this a problem for Coyne? No. Here is what Wikipedia has.

Another explanation for warning calls is that these are not warning calls at all: A bird, once it has detected a bird of prey, calls to signal to the bird of prey that it was detected, and that there is no use trying to attack the calling bird. Two facts support this hypothesis:

• The call frequencies match the hearing range of the predator bird.
• Calling birds are less attacked — predator birds attack calling birds less frequently than other birds.

Saying that the second item is a “fact” is a pretty strong claim, and seems to refute the possibility that warning calls endanger the callers.
More generally, however, it is the ease with which any “self-beneficial” argument can be devised that protects against the possibility that evolution could be falsified according to the terms of Coyne’s Point 2. There is some irony here as the main evolutionists to warn us about Just So stories were R.C. Lewontin and S.J. Gould. RCL was Coyne’s teacher and Coyne’s book Why Evolution is True is dedicated to him.
Moreover, a whole discipline (although a very undisciplined one), evolutionary psychology, has been built on Just So stories, and among evo-psych’s best-known critics has been Jerry Coyne (see his January 16, 2011, post).
Suicidal animals might fill the bill and prove evolution to be non-scientific by Coyne’s criterion. Here is Wikipedia on suicidal animals:

Pea aphids, when threatened by a ladybug, can explode themselves, scattering and protecting their brethren and sometimes even killing the ladybug.[3] Some species of termites have soldiers that explode, covering their enemies with sticky goo.[4][5] There have been anecdotal reports of dogs, horses, and dolphins committing suicide, but with little conclusive evidence.

But I am sure Coyne would be less than impressed by any such claims and would not react to them by consigning The Origin of Species to the dustbin. Stories could be concocted, and would be.