America does have pretty high suicide rates compared to international average, both teenage and general. However, it's hard to know if this can be attributed to gun availability, or if there are other factors at play. It certainly can't be solely blamed on guns (although gunshot is basically the most effective common suicide method). Scandanavian countries also have pretty high suicide rates, for example, even though guns aren't really common there. (Overall, I think Asian countries will have higher suicide rates than non Asian - possibly because it's culturally honorable?) I'm sure there is plenty of research done on these topics that should be easy to access.