I won't give a detailed answer to this question here (it seems to be no), but there is an article making the reddit rounds now that I need to kill before it becomes another meme (like that other badly reported story about psychiatry.)
The article is from BMJ 2002, called Influences of the Media On Suicide, and it puts its conclusion right at the top:
Reporting and portrayal of suicidal behaviour in the media may have potentially negative influences and facilitate suicidal acts by people exposed to such stimuli. Recent systematic reviews by others and ourselves (unpublished) have found overwhelming evidence for such effects.1 (emphasis mine)
And it offers about 8 references in support. And so now every nut with a microphone can proclaim it loudly: it's the media's fault.
We may want to take a pause and examine these 8 references: none of them offer anything close to "overwhelming evidence." For example:
Reference 1-- the one directly cited for the above statements-- is indicative of the type of "overwhelming evidence" that exists. The study finds that media reporting of suicide is extensive and detailed, but not that there is a clear link to future suicides.
In the summary, the authors use phrases like, "dearth of literature," "evidence is less reliable," "few studies permitting/demonstrating [the link]," "does not demonstrate consistency," "many studies fail to demonstrate" over 11 times in the 3 pages describing the studies.
Despite this, they are sure the link exists-- but they don't actually show the link, they infer a link. The authors repeat phrases, "it is fair to conclude that the evidence suggests an association [exists]" "tends to suggest," "probably reasonable to regard the association is causal" 13 times in two pages. Under these criteria, it's reasonable to assume the Matrix is real.
Reference 3 (not even linked correctly) is a letter to the editor, describing two cases, where the method of suicide was affected by internet, but not the decision to commit suicide. And the methods were rather weak: one guy took two pills of castor oil, and the other woman tried to drink water. No, I'm not kidding.
Reference 5 is frequently cited in support of media's impact. It supposedly says that a TV show with a Tylenol OD caused more Tylenol ODs: 20% of these suicidal viewers said it influenced their decision to attempt suicide in the first week post broadcast. Maybe-- that 20% is really 6 people. And most had attempted Tylenol OD in the past. Oh, and the authors note that while 17% of the suicidal viewers' choice of Tylenol was influenced by the show, some of them chose not to use it because of the show.
Reference 12 is probably the most cited reference in this field. In 1978 Vienna built a subway, which soon became a popular method of suicide. So the government established guidelines for reporting-- specifically, that the method not be mentioned-- and subways suicides decreased by 80%. Fantastic. Overall suicide rates didn't change, though. Too bad.
So much for the "overwhelming evidence" for a soon to be media soundbite.
The article doesn't make a good case for media influencing the decision to kill yourself, though I'll admit that it may influence the method. And that's where it gets tricky.
It's important to make a distinction between copycat suicides and copycat homicides: more poeple die in the latter, and, let's postulate, they didn't want to die. That has to be part of the calculus in media reporting. Copying suicide by water (instead of pills) is different than copying a 30 person massacre (instead of killing, say, one person.)
But you have to weigh this against the societal costs. The solution offered in these articles is to restrict media reporting. I think we can agree that the media are neither liberal nor conservative, but sensationalists, their bias is titillation. But to allow anyone, especially government, to affect the content of reporting-- literally, the information we are allowed to have-- seems exactly the wrong solution to a problem which may not actually exist. (e.g. I know it seems prurient, but I actually want to know all the details of David Kelly's suicide.)
Not to mention that if you say the media are partly responsible, then you're saying that you're less responsible.