There's a difference between CAN'T and WON'T. CAN'T is a possibilty. WON'T is a decision. CAN'T is less final. WON'T is more definite. If you clearly mean that there will not be a dog coming to your home at any time in the future, then you must communicate this clearly to your kids in a no nonsense, but not unkind fashion. You were the ones that opened up this possibility and gave them the hope, so be kind when you shut the door. Don't slam the door in their faces, but make sure it's firmly closed if you mean NO DOG.
'We have decided we will not (won't) be getting a dog. Our schedules are too busy, and it would not be fair to a dog to be left at home alone so much."
This sort of discussion is fair, kind, and probably truthful.
If the answer is CAN'T, then it could go like this:
"We have decided we can't have a dog right now. It's not a good time. We don't have enough time to research what kind of dog would fit our family. When we are ready to add a dog to our family, we will let you know and we can all start looking again. In the meantime, stop pestering us about it."