I would choose A actually.
'have' can use a gerund (makING) after it which, to me, sounds the most correct and makes the most sense.
With 'permit' you can also use gerund (makING) after it. However is sounds overly formal and in my experience I have only seen it with infinitive verb (I won't permit those children to make noise).
The other two 'let' and 'allow' - these can't use gerund (-ing) after so these can't be used in this sentence. However if you use the infinitive form (make/to make) then they are both fine: I won't let them make a noise/I won't allow them to make a noise.
So, I would actually choose answer A. But as I'm sure you and everyone else are aware, the variations in the English language around the world will probably justify the use of the other answers in some way or form also.
HtH - Rob.