1: prevent the cause, not the effect. If your country experiences many suicides due to harsh working conditions, introduce some new rules or cultural changes to make work more bearable. If people want to die due to extreme debt, or inability to afford medical treatment, or monetary reasons, then fix the economy or at least target certain problematic aspects of it. If people want to die due to unchangeable genetic problems, well... I suppose it can't be helped, or maybe it can be via a genetic screening program. Either way, don't just prevent suicide, prevent people from wanting suicide in the first place.
2: offer a safe, informed, and responsible way out. This might seem counter-intuitive, but I think it could potentially work. Think about the reason for this site's existence. It's because you're not allowed to talk about suicide anywhere else, otherwise you get treated like a crazy person possessed by the devil. You get told that "that's not you talking, that's just your depression" and all that. Instead, if society were less judgemental, and we instead made people sign up for a 6 month program where they go to group therapy with their loved ones and everyone is instructed on how to handle grief and loss and all that... It could lead to the person dying anyway, and those close to them would at least be prepared for it. Or, it could have the opposite effect, especially on people that might have otherwise made an impulsive decision. They would be shown the implications of them dying and they would have the time to realize it's a bad idea, and they would be able to see all this because they were allowed to open up about it. Again, it doesn't initially make sense to say that creating a path to a more responsible suicide could actually reduce suicide numbers, but I think it's possible.
3: In the absence of the last option, I like what someone wrote earlier in this thread about hotlines and stuff being shown in popular jumping spots or whatever. It's non-coercive and completely optional. However I think it's possible that those numbers might be dismissed because the jumper might not take those hotlines seriously and it feels very impersonal. Instead, there could be posters or just text saying "have you made your last conversation with your family yet?" "Do your friends know?" "Have you written a note?" "Do you want to be found like this?" just various short things to make the person think about if they're actually ready. If they are, and they're sure this is the method they want, then oh well, they're dead. But it's a preventative measure that could be more effective than just posting the anti suicide hotline. Plus, not everyone has a cell phone to call the hotline anyway.