From that Harvard report....
"We performed reviews of the academic literature on the effects of gun availability on suicide rates. The preponderance of current evidence indicates that gun availability is a risk factor for youth suicide in the United States. The evidence that gun availability increases the suicide rates of adults is credible, but is currently less compelling. Most of the disaggregate findings of particular studies (e.g. handguns are more of a risk factor than long guns, guns stored unlocked pose a greater risk than guns stored locked) are suggestive but not yet well established."
Harvard School of Public Health » Harvard Injury Control Research Center » Suicide
It is a very interesting report but one which admits the lack of correlating facts to reach firm conclusions.