Suicide can be accomplished by any number of methods. A quick Google search will show that. However your question as I interpret it is would making firearms unavailable reduce suicide.
Suicide methods***snip***
Firearms***snip***
Research published in the New England Journal of Medicine and the National Academy of Science found an association between household firearm ownership and gun suicide rates,<11><12> though a study by one researcher did not find a statistically significant association between household firearms and gun suicide rates,<13> except in the suicides of children aged 5–14.<13> During the 1980s and early 1990s, there was a strong upward trend in adolescent suicides with a gun,<14> as well as a sharp overall increase in suicides among those age 75 and over.<15>
Two separate studies, in Canada and Australia, conducted in conjunction with more restrictive firearms legislation, demonstrated that while said legislation showed a decrease in firearms suicide, other methods such as hanging increased. In Australia, the overall rate of suicide actually increased (following a trend that had been moving upwards for some time), and did not decrease until measures specifically aimed at providing support to would-be suicide victims was enacted.<16><17><18>...emphasis addedResearch also indicates no association vis-à-vis safe-storage laws of guns that are owned, and gun suicide rates; and studies that attempt to link gun ownership to likely victimology often fail to account for the presence of guns owned by other people.<19><20> Researchers have shown that safe-storage laws do not appear to affect gun suicide rates or juvenile accidental gun death.<19><20>
http://en.wikipedia.org/wiki/Suicide_methods#Immolation The article you blind linked to at
http://www.thestar.com/opinion/editorialopinion/article/1077286--gun-control-keeps-suicides-down disuses the impact of repealing the Canadian Firearms Registry. To draw any conclusion from a article that is obviously trying to preserve the federal gun registry in Canada proves little as the author obviously has an agenda. Without knowing other factors that might have existed during the same time frame that might have effected the suicide rate it is hard to come to a definite conclusion. For example during the same time frame that the firearms registry was passed into law in Canada an organization known as CASP was actively trying to reduce the suicide rate. My link above mentions that such efforts often are very helpful.
The Canadian Association for Suicide Prevention (CASP) also a national non-profit organization was incorporated in 1985 by a group of professionals who saw the need to provide information and resources to communities to reduce the suicide rate and minimize the harmful consequences of suicidal behaviour.http://www.suicideprevention.ca/Interestingly enough the suicide rate in Canada is HIGHER than in the United States. I mention this only as a factoid as it is futile to compare such items in nations that have far different societies with many factors influencing the results. For example why is the suicide rate in Japan so high?
Why So Many Suicides in Japan?
It's the economy, stupid. And the health-care system. And the religious beliefs. And the … ***snip***
There's no single factor, but experts point to a combination of economic woes, poor mental-health resources, lack of religious prohibition, and cultural acceptance of the practice. * The economic recession that hit in the late 1990s seemed to increase the number of suicides, which jumped by 35 percent in 1998. Japan's high-interest loan system and historically strict bankruptcy laws may have contributed to this effect. But the Japanese suicide rate remains elevated, even though the economy has since recovered. Even before the recession, the rate was already a third higher than that of the United States. (Not that Japan is setting any records: Hungary, Estonia, and Latvia, among others, have more suicides per capita than Japan.)
http://www.slate.com/articles/news_and_politics/explainer/2007/05/why_so_many_suicides_in_japan.html To be fair, improving our existing laws such as the NICS background check might have a positive impact on suicides accomplished by using firearms. But setting up programs to help potential suicide victims couple with commercials promoting those organizations of TV might have far more impact.
The Brady Campaign has made efforts to improve the NICS background check to better filter out those people who have severe mental issues. In this case I fully support their effort.
POSITION: The Brady Campaign supports strengthening the Brady background check system to make it harder for criminals and other dangerous people to buy firearms. The Brady Campaign supported the NICS Improvement Amendments Act of 2007, which provides for financial assistance to aid states in sending records to the National Instant Check System (NICS).
PROBLEM: Many states fail to supply complete records of prohibited gun buyers to the national Brady background check system or the Brady Law's National Instant Check System. That means many felons, domestic violence abusers, and those who are dangerously mentally ill can walk into a gun store and buy firearms without being stopped.
The Brady Law, which mandates that federally licensed firearms dealers do background checks on prospective gun purchasers, has prevented over 1.9 million prohibited persons from buying guns. However, a background check is only as good as the records it can search. Unfortunately, many prohibited persons are not blocked from buying guns because their records are not in the NICS, including about 80-90% of individuals with disqualifying mental health records, and one-fourth of those with felony convictions. Ten states do not provide any relevant domestic violence records that indicate prohibited purchasers.
http://www.bradycampaign.org/legislation/nics/