If you get into discussions with believers about what evidence would convince you that the god they believe in exists ... you may be literally speechless, because, depending on which god, and which religion, and which denomination, and which congregation, and the disposition and experiences and perceptions of the person asking the question, you really, REALLY don't know what they're asking. The god they perceive may be entirely different than that of their brother, or mother, or father or sister or child's.
But here's how I might answer:
First I'd stipulate that the god that we're talking about is Yahweh as depicted in the Old Testament (and modified by the New Testament). Second, I'd define evidence as a repeatable, independently verifiable test that uses a prediction relying on the existence of this god that will yield a pre-defined consequence - first time, every time, to a reasonable certainty. Third, let's stipulate that the test result can only be produced by the action of god, and cannot be explained by common natural phenomena. Fourth, "reasonable certainty" means some level of repeatability - for me, 99 out of a hundred times is acceptable. For the wider world to accept this, we might try the same test thousands of times and expect no failures before we'd publish the result ... but I'm looser than they are.
Let's try a thought experiment ... If God Exists, and He is all-powerful, and He answers Prayers, then I ought to be able to construct a test whose results would signal to me that God answers believer's prayers. Use an Iraq War amputee as an example ... this brave man or woman lost a limb in the service of their country, and deserves our profound respect and thanks, and we as a grateful nation should demonstrate our appreciation. Therefore:
1) a single Devout Believer should sign an affidavit that they will pray for the complete restoration of the Veteran's limb, and that this restoration of the limb will occur without human intervention within one month of the date of the prayer being offered to God.
2) at the completion of the prayer, the Devout Believer signs an affidavit that affirms that the Devout Believer has offered the aforesaid prayer of limb restoration to God on behalf of the Veteran.
3) at the end of a month following completion of the second step, the Veteran is inspected for restoration of the previously absent limb.
4) if the previously absent limb is restored, then we may say that the hypothesis "God exists" is true, contingent on successful repetition of the test using another worthy Veteran and another Devout Believer.
5) if the test only succeeds once, we may not conclude that God undeniably exists, but we can all agree that this was truly a wonderful miracle, and the hypothesis "God Exists". although not proven to a reasonable certainty, still warrants that believers and non-believers alike adhere to Pascal's Wager and live their lives as if God Exists, for He has given us a sign.
6) If nothing happens, then everyone agrees that it's all bullshit.