This is an interesting question. Jerry Coyne gives a list of seven pieces of evidence that, if replicated and confirmed, he would find persuasive.
- Fossils in the wrong place.
- Adaptations in one species good only for a second species.
- A general lack of genetic variation in species.
- Adaptations that could not have evolved by a step-by-step process of ever-increasing fitness.
- The observation that most adaptations of individuals are inimical for individuals or their genes but good for populations/species.
- Evolved “true” altruistic behavior among non-relatives in non-social animals.
- Complete discordance between phylogenies based on morphology/fossils and on DNA.
These are just the headings. In his post he elaborates on what they mean.
Of course, when we look at the history of science, we see that theories are never disproved in isolation, leaving a lacuna. It is always the case that a theory is rejected because of the presence of a stronger competitor. So even if there is evidence for any of the above, this by itself will not be sufficient to reject evolution if there isn’t another and better theory waiting in the wings, ready to take its place.