This is one that's been going through my head a lot. Partly it's the sort of "that's what I should have said" frustration, only in this case the frustration is not having been present at a couple of discussions. In these particular discussions a friend of mine who has and continues to do excellent work on sustainability has run up against some climate change deniers, which for my friend was quite upsetting. I on the other hand tend to think "fresh meat" when one of these curious creatures pops up. Though I will admit that I am often just as frustrated, usually because anyone who is a climate change denier at this point has some kind of major irrational block that it would take a talented psychoanalyst to work around – that is they are beyond convincing.
But the thought I wanted to share was this: when people claim that you can't prove that climate is happening, it is entirely acceptable to counter with "Well prove that it isn't". You can treat it just as you would claim any fringe claim (why do you ask me if I can prove UFOs don't exist? Its YOUR job to prove that they DO). The weight of evidence is now overwhelming, and anyone would be hard pressed to find examples of ice that ISN'T melting, water that ISN'T getting scarce, or ecosystems that AREN'T collapsing.
Furthermore this is a perfectly acceptable experimental method known as the null hypothesis. It is a partly psychological thing – you choose a hypothesis which is generally the opposite of the discovery you want to make, and try to prove it is true. This means that you aren't attempting to prove that the result you WANT to be true IS true, and so are less likely to jump to conclusions. The idea is that if you cannot prove your null hypothesis, then (roughly) its opposite is true. Therefore anyone should be happy to look for proof that climate change isn't happening – deniers and normals alike – but it is a simple fact that it is not a hypothesis which can be supported.
A final point: even though rarely voiced, much of the denier movement recognises this on some level. Why is so much of the denial rhetoric about attempting to pick holes or magnify uncertainties in the climate change predictions rather than compiling and presenting demonstrating that climate change isn't happening? Simple: because there is no such evidence.