Don't punish mistakes, but do (always) reward honesty and responsibility. There is a good chance that the children are refusing to tell because they feel they will get in trouble. In the case of an actual accident, this is unfair as the child is receiving punishment for something it cannot be held responsible for. Responsible behaviour also means understanding when someone could not reasonably have known something and not faulting them for it.
When kids start to understand that being open and honest about mistakes gets them rewarded even when they have broken something, they'll be more likely to speak up. This is a good thing in the long term, because you'll understand what caused the accident and can perhaps prevent it from happening again in the future.
And even if the kids are knowingly breaking the rules and this has caused the problem, you should still reward honesty. It will still teach them that even if they did something they should not, being honest is still better than being silent. In such a case, reduce the penalties for breaking the rules. Be explicit about it, to.
After this, whenever a situation comes up where the kids still will not speak when something happened, openly tell them that if they will not speak up you will assume the worst and act accordingly. When they reach the age of basic math they will quickly learn that this is the worst possible outcome.
The system rewards openness and responsibility as long as it is used correctly. This is a thing we strongly strive for in my job and always rewarding honesty while not punishing mistakes really helps people feel more responsible and open.
(with random amounts of marbles, I don't know how many you use, it'll work as long as the relative amounts stay about the same)
Kids accidentally break a vase and confess: Add 2 marbles for being honest. No punishment since they couldn't help it.
Kids break a vase because of playing football inside, which they are not allowed to do and confess: Remove 5 marbles for breaking the rules, add 2 marbles for owning up to it. Make sure you mention both counts and don't just remove 3; they have to know that being honest is helping their case.
Kids accidentally break a vase and don't say anything: Tell them you are assuming the worst if they don't explain. Then remove 5 marbles for intentionally breaking the vase.
Kids break the vase because of playing football and don't say anything: Tell them you are assuming the worst if they don't explain. Then remove 5 marbles for intentionally breaking the vase.