According to Tae Kim, there is a negative volitional form, but it is archaic and formal, so you're better off using the modern expressions given by the other answers.
However, it does show up every now and then (トキ in 北斗の拳 seems to like using it), and it's a pretty simple conjugation, so it's worth knowing.
To form the negative volitional, you add まい to the end of the verb. If it's a る verb you drop the る first, so 食べる -> 食べまい. If it's an う verb, just add it to the end, so 探す -> 探すまい. する and くる become するまい and くるまい (isn't it rare that they fit the pattern governing the other verbs?), and you add まい after the ます form for politeness, 死にます -> 死にますまい.
examples from 北斗の拳:
こんな馬にまたがる男はひとりしかおるまい
おまえたちと同じ地上に降りたたねばなるまい！！
その棍棒が血ぬられることはあるまい！
しかたあるまい