Why do beans squeak?
From my experience, this is more likely to happen if the beans are cooked in a dry manner (eg as part of a pie filling, in a very thick sauce, or by sauteeing or baking) than when they are boiled - so par-boiling the beans before adding them might silence the squeak somewhat.

Also, the texture (and colour) of cooked grean beans is known to be somewhat pH dependent - if you are cooking them in a rather acidic sauce (eg one that has wine, vinegar, fruit juices ... added to it), you might also want to consider parcooking your beans separately.