I have been doing a lot of thinking about how I would respond to a suicide in my parish. Let me be clear that I do not believe anyone in my parish is having such thoughts, but I have been doing some historical research on how the Church has dealt with the issue over the centuries. This was spawned by a discussion I had some months ago with a priest out on one of the reservations in this state who was constantly having to do funerals of suicide victims. For a myriad of reasons that I won't go into here, suffice is to say that this is an epidemic problem facing Native American reservations these days, particularly amongst the young.
By the grace of God, I have never had to pastorally face that scenario as a priest directly (and I pray I never will), though I have had to deal with it personally more than once from friends who have taken or have thought about taking their own lives. For my own pastoral ministry, I have thought it was important for me to research some of these issues before I am confronted with it without having done serious thinking on the issue.
Sadly, the Church has often taken some very hard line views of suicide, ironically, on both ends of the spectrum. The classic Catholic understanding was that suicide was the unforgivable sin. Mortal sins, according the Catholic moral theology, are grievous offenses that are taken after sufficient reflection and have been done with full consent of the will. Unlike other mortal sins that can be repented of and absolved after the fact of its occurrence, suicide, by its very nature, does not allow an "after the fact" possibility of reconciliation and forgiveness because the person is dead. Since you cannot repent of sins once you are dead, then suicide by inference must be the unforgivable sin, as the logic goes.
I have to admit that I have much trouble refuting that line of reasoning because it is extremely logical and I am hard pressed to deny it. Life is a gift, and we are never suppose to take life in malice aforethought, to use the old language of English common law. If I was trying to refute the theological premise of the above argument, I would probably highlight the fact that it is completely lacking in any mention or application of God's grace and can be viewed as somewhat legalistic in application.
Certainly the Church over the centuries has applied that logic in very cold hearted ways, denying suicide victims a proper Christian funeral or burial, to the point of being hateful about it. I have heard tell of priests or pastors making the surviving family feel like it was all their fault, amongst other horrors. When otherwise sound doctrine is applied in cold hearted and hateful ways, God is not glorified and the Kingdom of God is not enlarged.
Suicide is a thorny issue. In the 20th century, the Church in its quest to embrace Modernism and "relevance" has been tempted to swing the pendulum to the other side of the spectrum, making, in effect, suicide into the one universally excused sin, no questions asked. We look to the sciences and psychology and to the memory of bad doctrinal application by the Church historically, and our knee jerk reaction is, "Well, it is not a sin because they were clinically depressed or not of sound mind because of some other medical condition. So, therefore it is not their fault and this person is in heaven now." I have heard more than one sermon on the subject say exactly that.
Both of these pastoral applications tend to leave a bad taste in my mouth. The former seems to leave no room for God's grace, but the later seems to be a weird, shadowy reflection of judgmentalism, just in reverse. If the Church is wrong to condemn a suicide victim to hell because they took their own life and therefore must not have been forgiven, I think the Church must also be wrong to simply preach the person into heaven, assuming that suicide can never really be done of one's own, free will. We like to think that condemning someone to heaven as opposed to condemning someone to hell is somehow more virtuous on our apart; but the motive is the same in either case though. In both instances, the Church is playing God in that we are being the ultimate judge and arbiter of the person's soul. That's not our job but God's.
About the most digestible resource I have found on the subject is a pastoral letter that was put out some years ago by the Bishops of the Eastern Orthodox church. You can read the text of it here. It is short, but very well reasoned, very powerful, and premised on Holy Tradition as well as Scripture. I commend it to your reading.