When can a monopoly's marginal revenue curve be upward sloping?
Because the marginal revenue curve is correlated with the demand curve (the MR curve always has twice the slope of the demand curve), the MR curve will only be upward sloping if the demand curve is upward sloping. This means that there must be a situation in which the quantity demanded actually rises as the price of the product rises.
The only way for this to be possible is if the product is a giffen good. Giffen goods are exceedingly rare in the real world because they must be inferior goods for which the substitution effect is weaker than the income effect as the consumer's income goes down and the price of the giffen good goes up.