I know this sounds like such an amateurish thing to ask.  I've probably been in close to 30 plays and have never had this problem before.  I'm in a production of "Inspecting Carol" and many members of the cast (including myself) are having a huge problem not laughing.  The play is pretty funny itself but the actors are also just hilarious.  In the case of some of them, all I have to do is look at them and I start laughing. 
Somebody half joking mentioned thinking of dead kittens to get through it.  I love kittens but I tried it anyway and it only half worked lol. 
We open in two weeks.  Maybe by then, we'll get it together.  Maybe an audience will just cause us to be in check but if not, does anyone have some tips on combating the laughing problem during a performance?

All good points.  Thanks!

My two bits:

1. As the repetition settles in, as long as things remain consistent, you will to some extent desensitize to the point where it shouldn't be a problem.

2. Stay in character.  If your character's not supposed to be laughing, there's a reason for it.  Is there something detrimental going on?  Are they confused?  Missing information to complete the joke?  Distracted? Just dim? Follow THAT and you should be in the right frame of mind of also not laugh.  And if not... well, make one up, or justify why they WOULD.

I think the tricky part in all of this is that the actors still need to "be" funny for the audience's benefit, while not succumbing to the humor of the moment. The repetitive nature of rehearsal helps with the latter, as they know the "joke" is coming, but it can also lead to drying up of the delivery. Typically, I've seen hilarious first readings that break everyone up with all the freshness that's there, and that freshness starts to diminish with the repetition. That's one of the biggest challenges to the actor - stay funny, but don't lose it on the punchline.

The characters, on the other hand, even in a farce, must always be in a serious moment, as edh915 notes.  A viewing of any of the long-running sitcoms (Cheers, Seinfeld, Friends, Raymond) will attest to that. With exception of the "wise-cracking" character whose lines are obviously meant to be funny for the benefit of the characters, the rest are in serious mode, the plot at the point meaningful and weighty, as silly as it may appear to us viewers. Another challenge to the actor. 

Re: "as long as things remain consistent" - aye, there's the rub. Once the lights go up and the audience starts responding, and the actors begin to hear laughter in such measure that they haven't heard through rehearsals, that freshness resurfaces a little and the comedic edge sharpens.  A new delivery, a different reaction, a timing that really hits the spot, all of these present to the cast a new "punchline", something they haven't been ready for, and the difficulty of not breaking character comes back to haunt them. I've experienced it first-hand.

My advice? If you feel that "break" coming on, try to find a diversion (a reason to look away from the other actors, perhaps a glance at the set, or casually handle a prop), something that does not appear out of character nor distract from the attention of the audience, and then hurry up and collect your wits about you.

Most of the time, I've found that the funniest things on stage are the way the actors look, their physicality, their facial expressions.  Remember, despite the amount of dialogue, theater is a visual medium.   When a friend tells you about going to the theater, they say "I saw a good play last night", not "I heard a good play last night."  Try not to watch the play you are "in".