Regardless of whether you have to show best interest of the child or a change of circumstance to modify a particular custody order, what I have found to be most effective and successful way to modify custody is to use, what I call, the incremental approach. This method takes the “meta” view of the custody order and all the players involved.
Rather then request a significant change in the child sharing arrangement(i.e. alt. weekends and every Wednesday overnight to alt. weeks) you request something that is a natural outgrowth from the existing order—using the above example, you would request moving the every Wednesday overnights to Thursday and a Monday overnight tacked on to your weekend. As such, on your weekend you would have the child Thursday to Tuesday morning and every Thursday.
This request is child focused in that the change is not that different from the schedule the child is used to and doesn’t require the Court to make a radical change/modification. Plus, it gives you the added benefit of having a success in court— so that in the future, when you want to get more time the other side will recall how the court viewed your past request as reasonable, and they may approach your new request with more openness.