Ok, after this discussion in the thread and some deliberation on my own, I have decided that the best course of action to take is to Ban Blissey and Chansey. As Shonen Bat and others have said, both are very powerful on their own, and almost necessitates the usage of Conkeldurr or a Blissey of your own, and skews the battle into "whichever team has their blob die first loses".
Tagging The Immortal to get this ban implemented on showdown.
If you think this is ban is an incorrect course of action, or if you have a better idea, discuss it here.
Other than that, discuss the meta post-Blissey and Chansey ban