For a start, let's divide miracles into two types; the once-off miracle, which happens only once and cannot be reproduced under laboratory conditions, and the repeatable miracle, which happens every time the right conditions are in place.

I can see a couple of issues with this formulation, defining a miracle for the moment as a suspension of natural law by divine fiat. First, while a one-time miracle presumably wouldn't be reproducible under laboratory conditions, most miracles that I can think of would leave an inconsistency with known physical law and could be analyzed by working backwards from the available evidence. Some would be more obvious or easier to evaluate than others; if the face of the Virgin Mary appeared in my cornflakes one morning, I'd have only until they got soggy to publicize the event, but if a volcanic eruption in Luzon generated a pyroclastic cloud that scoured the rest of a town down to bedrock but left every board of a flimsy wooden church unharmed, there's still plenty of lahar sediments to analyze. You don't need to grow evidence in a Petri dish for it to be real science.

(Though it's worth mentioning here that lots of religions, plus Charles Fort, allege odd phenomena. Incorrupt corpses are alleged for a number of Catholic saints, for example, and the corpses in question certainly look less corrupt than I'd expect them to be, but they also show up among Buddhist monks.)

Then there's the idea that miracles might show signs of agency, i.e. be directed at some goal; God's motives in the context of Christianity are of course famously ineffable, but the miracles alleged in the Bible do show certain patterns (protection of the innocent or of a chosen people; glorification of God; etc.) and we might reasonably expect these to continue. We can pick these out with statistical methods: if preachers of one particular sect are indistinguishable from those of another in terms of habits and demographics and there's enough of both to make a good sample, but the rate of lethal accidents for one is zero, that's certainly suggestive.

Finally, many alleged miracles are persistent in time but limited in space: Lourdes water, weeping statues. These leave an inconsistency that's laboratory testable (many have been tested, generally with negative results) but wouldn't be factored into models of physical law, or which at least would lead to much less elegant physics than we observe.