In short, no evidence would convince me otherwise, thus making me a maddeningly difficult person to argue with. I think a great deal of evidence favors Creation particularly abiogenesis and the lack of a consistent evolutionary fossil record so say the ability to produce life from non-life and a better explanation for the lack of a fossil record I would find to be very difficult to counter even if I felt bound by the biblical account.
Presently I think that unquestionably the genetic evidence is the most difficult for Creationists to answer particularly things like the apparent chromosomal fusion between two existing ape chromosomes to form a human chromosome. Interestingly at the same time, I think some of the work in master regulatory transcription factor genes offers a potential solution to a difficult problem for Creationists: how did we get such biological diversity in such a short period of time from the ark? I also find the dating methods to be difficult to deal with since I am a biologist who hates math and not a physicist. I have heard from creationist physicists who I trust that there are reasonable arguments to be made against it but I am essentially taking them at their word since one can only be an expert in so many topics.
Ultimately, science is fallible because scientists are fallible and I believe God's word to be infallible so when they seem to be in conflict I will of course go with the latter.