More religious countries may have lower incidents of suicide but they don't seem to be enjoying the life they do have as much as the less religious countries. None of the top 10 countries according to the World Happiness Report[1] are religious. On the other hand, of the top 10 religious countries, according to your link, the highest ranked for happiness is Thailand at 34. This shouldn't be terribly surprising since it is a deadly sin to commit suicide in most of the Abrahamic religions and the more devout you are the more likely you are to adhere to this particular tenet.

[1] http://worldhappiness.report/ed/2015/

Or all the unhappy people in the happiest countries killed themselves.

80% of the US is affiliated with a religion.

Self identification, affiliation, and membership are not synonyms.