if one does not have a belief in hell then i cannot see how such a consideration would ever come about. in any case, i would agree that it is usually the case that severe suffering is the motivating factor that causes a being to end their life.
i hope that you appreciate that the "unreligious" (which i understand you to mean monotheistic) don't have a belief in God and thus arguments which rely upon that belief are hardly going to be effective in preventing someone from taking their life. would you agree?
i grew up in Libya and spent years at the mosque. i've studied Islam as an adult for two decades and, yet, i remain unconvinced of it's veracity. nevertheless, i would prefer if we could leave such discussions for areas of the forum which are more appropriate. i'm sure you understand.
believers in God can be 'non-religious' too such as the general people in the world these days who believe in God but yet live very secular lives with religion playing a very little part in their lives if at all
So i take it by 'non-religious' you meant athiest
to an athiest i'd say, if you dont believe in God then you dont neccessarily have any objective truths; all is subjective for you, so there is no point in anyone trying to convince you that suicide is wrong, for you will only accept it if it suits your desires, for that is the basis of your subjective reasoning; accept whatever you please and 'deconstruct' whatever that dont
As an alternative, i'd tell him that there is overwhelming signs/evidences in the universe/creation that God does exist and there is an objective truth, thus he should search this truth out in all sincerety in order to find out the truth concerning any matter
I would have also told an athiest to trust more in his intuition; what his inner self tells him about this issue for it well could fall under the more obvious right and wrongs, but in the words of a great Scholar, there is a chance of appealing to someone's innate nature before he has reached the level of a PHD [reffering to the 'there is no objective truth' principle which it incorporates] for the PHD is 'when the cement is poured on it'! , however if it weren't aquired by a phd, then it may not be intensely indoctrinated thus there might still be a chance