I used to coach tennis. Sometimes at the end we'd do a game. Almost without exception the girls had to be persuaded to play as they said "I'm not good enough", even in the all girls group.
The boys I'd more often hear the phrase "What will I get when I win?" Not every boy by any means, but a good proportion of them.
The girls more often won, so it wasn't that they were weaker either.
There will be an aspect of them setting each other off. One says they're not good, and others think either "she's better than me, so I'm really bad" or "I have to say that too or I'll seem arrogant".
Also I tended to do myself down at any test on the basis that if I did badly then I could hide my disappointment in saying "oh yes, I knew that".
I'm not sure telling them they're amazing etc will have any effect. Wouldn't on me. They'll just go "yep, miss always says we're great whatever we do. That's because we're so bad she doesn't want to discourage us"
Perhaps showing that they're good in other ways. "That essay was really good. Would you mind if I photocopied it so I can keep it as a really good example?" type thing.
Positive reactions on specifics.
I remember being really boosted when we were doing posters for the wall for open day and the teacher came past looking at books and stopped the poster I was doing and asked if I could do it on something I'd done for homework because what I'd done was so good. (I can even remember what it was-on crystals!)
Another time I remember our class being told that we'd done so well on a specific topic that they had brought in an expert to talk to our class, and at primary we got an extra trip out because "they knew our class could be relied upon to behave"
If you don't do them all at once (or they'll see through it) but try and make sure over the year you give each of them a specific praise. I think that will give them more confidence than just telling them they're good.