Your suggestions are not wrong, (well, Ayez du beurre); but the infinitive, as shown here, does work just as well: http://french.about.com/od/grammar/a/givingorders.htm
That would be in the imperative, though, not the infinitive. Really, 'have some butter' (or 'have butter') isn't a particularly correct translation, even though Duo currently accepts it. @Cyndiluwho -- you're right, it's not a complete sentence, but it is a proper phrase (in the English sense of the word). For example, if you put something with a conjugated verb and a subject in front of it -- such as 'je peut' / 'I can' -- it works perfectly fine ('je peut avoir du beurre' / 'I can have butter').
The infinitive can be used to give commands just like the imperative: http://french.about.com/od/grammar/a/infinitive.htm
I mean -- I'm not sure about 'just like the imperative'; the imperative and the infinitive-command structures aren't totally interchangeable. But, yes, I see what you're saying. Although I still can't imagine any situation in which the concept of having butter would be best expressed in the infinitive-command ...
Well, Laura Lawless does say at one of the links I provided that the French infinitive...
... can be used several different ways without any conjugation [such as]
in place of the imperative for impersonal commands (as in instructions or warnings).
Mettre toujours la ceinture de sécurité. Always wear (your) seatbelt.
Ajouter les oignons à la sauce. Add the onions to the sauce.
So in the case of impersonal commands, it appears that the infinitive CAN be used interchangeably with the imperative.
@mere_des_chats: by 'the imperative and infinitive-command structures aren't totally interchangeable', what I meant was that they aren't totally interchangeable, i.e., while there are situations in which they're interchangeable, it doesn't always make sense to swap out one for the other. This struck me as one of those cases where the infinitve-command didn't make sense; but I never suggested that there were no cases in which it would make sense.