Here he is back in May when Comey just got fired.
"Trump Backs Deputy AG on No Special Prosecutor for Russia Probe"
http://www.newsmax.com/Politics/trump-rod-rosenstein-russia-probe/2017/05/12/id/789910/
So what turned Rosenstein? I see Senator Warner DU pressuring Rosenstein that the Dems would not confirm any FBI Director that Trump appointed. Warner wanted him to appoint an SC. He may have gotten much more pressure.
Probably several factors, or sources of pressure, and some we might not even know about. But he made the appointment just a very few days after Trump fired Comey and Rosenstein became fairly controversial in the news.
There was the report that he talked of resigning during the confusion about what part his memo played in the decision to fire Comey. And he was very flustered during that time, and suddenly we had a SC appointed.