What a great question! I will answer it directly - but first give me a few lines to lay out the (some obvious) ground rules:
1. Once the genie's out of the bottle there's no getting back in. The US, UK, India, etc. are highly, highly unlikely in the absence of a "better" technology to disavow themeselves of nuclear capacity.
2. Who decides what is "allowed"? The UN, the US, the nuclear club?
3. Every country has a right to self-defence.
Now, given the above - it being of sober and unbiased mind - I see no reason why most of the world, with the example set by the most powerful nations, shouldn't be "allowed" to develop nuclear weapons.
I wouldn't want NK to have nukes - but what do you say to them directly? Nothing - you can't reason this out. Luckily most of the world don't want NK to have nukes either, which is good because they'll support any sanctions/inspections we want to demand. They'll support that because NK are a highly oppressive, unpredictable and glory seeking nation.
Now Iran. Not quite in the same league as NK. Not quite the same level of support. Never going to stop them getting nukes in the long term IMHO.
Now Japan. They don't want nukes. If they did they could do it quickly and easily as no-one could deny them for long.
So.
I think that quasi-universally condemned, isolationistic, unpredictable and oppressive regimes should not be allowed nukes (NK springs to mind without consulting the CIA world factbook).
I wouldn't like countries hostlie to my own to obtain nukes (good old spying and subterfuge works in the short term here) but I can see real reason to actually deny them.
Solution - the only solution - is to try to talk around nations or force them into isolation due to a universal distaste of the international community.
Don't see any other options.
Andy
EDIT: The nuclear club scaling back it's arsenal at every level would also be a good thing for the short term (ie no small nuke developments).