"contrary example" is correct and can be used in written English.
You can use it when you are introducing or pointing out an example that is opposite or different from what has previously been mentioned. For example, "I thought that all cats liked fish, but my friend's cat is a contrary example—it absolutely hates it."
Or, as a contrary example, Christmas decorations are made throughout the year, but their sales are concentrated in a four- to six-week period.
There is mixed evidence on whether extended nomination battles tend to hurt the party's candidate in the general election; the Democratic race between Barack Obama and Hillary Clinton in 2008 is often taken to be a contrary example.
While "MDNA" falls to No. 8 this week, and "Born This Way" sits at No. 161 in its 46th week out, the biggest contrary example of this trend is sitting pretty at No. 2 — Adele's "21" (XL/Columbia) had no extraordinary marketing when it came out last year, and no sales gimmicks, but it has barely budged from the Top 5.
We give a contrary example as follows for the proof of Proposition 3.2.
Consider the contrary example of The Baltimore Sun.
The only contrary example in recent years was when President Barack Obama tossed the issue of Syria's use of chemical weapons to Congress.
But undoubtedly, there are contrary examples.
Contrary examples like Raymond Carver, who wrote almost no piece of fiction longer than a dozen pages, tend to confirm the rule.
Avoiding evil suggested a pretty low bar, but the vow itself — along with the founders' boast that "our business practices are beyond reproach" — was an invitation to find contrary examples.
This windowing strategy has become increasingly common, although there are enough contrary examples of albums that sell many copies and are also on Spotify — like the latest from the British band Mumford & Sons — that the issue is considered far from settled.
But I haven't seen much research on the topic, and it is easy to think of some contrary examples (for instance, Sarah Palin was very popular in Alaska in 2008 but played poorly on the national stage).
