Ezra says that governors shouldn't be appointing senators, which seems good on general democratic grounds. Advantages as awesome as Democratic incumbency in New York should not be attained by gubernatorial appointment. But since it takes time to hold a special election, this would condemn states to a period of senatorlessness.
Maybe the best solution would be to require that appointed Senators may not run for re-election. The only real disadvantage I can see here is that if one person was the absolute best candidate, the state would be deprived of the optimal candidate's service during either the pre-election or post-election period. But I don't think that clearly optimal candidates are very common in our world.