Defining a miracle as an unlikely event with a positive outcome really is grasping at straws.
It really depends. If you think what people knew 2000 years ago, many things we now think as normal would have been miracles then.
There's also possibility to use the word "miracle" in normal everyday language without religious overtones at all. Suppose I needed money for a medical operation, found a coin in the street, decided to play lottery and won the money for it. I could say it was a miracle, and still think that it was nothing supernatural.
Or you could do some experiments and notice some tendency. You could notice that all the perfect numbers are even, and call it a miracle. You could notice something in real world experiments you can't explain and call it miracle, or say that it would be a miracle if they weren't caused by something. (And notice that I don't mean they'd be "supernatural", just that you can't explain them).
From religion's point of view, why should divine miracles be (obviously) contrary to the scientific knowledge? Maybe it would be stronger message from God to give real blatant miracles, but then he could just inform us about his being and thoughts straight forward. It would perhaps be problematic for the stereotypical religious person, but I at least can imagine a world where God chooses not to care of making himself known all the time.
Anyhow, I don't think that supernatural miracles would be in any way necessary for religion.
Also, I don't think there's any reason to think science and religion would be incompatible. You could for example think that the area of religion is in those questions where science is silent. Why there was a Big Bang? Why is there something rather than nothing? How should one live his life? (I don't know what's the current thought about the first question, or how silent science is about it, but the point is probably clear: there are things that science doesn't even try to say anything about).
I don't think there's any
need to insert God into those things, but neither that there's anything that stops someone from doing it.