Some (probably impossible and maybe bad) ideas:
-Stop the exchange of a coin temporarily when a coin hits a given increase/decrease in a predetermined time (say random 30% in 1 hour);
-Give a minimal required marketcap before coins are added to the big trusted exchanges (say random 40 million);
I'm curious for your insights.
Since there are decentralized exchanges your first point isn't possible. As for a minimal requirement on big exchanges, they already do that to an extent either through listing fees or by wide community requests. A minimum marketcap doesn't make sense though as it tells nothing of the volume and it can be much too easily manipulated.
I don't have a better solution though, there will always be shitcoins around.