You can still tax resource extraction industries in your country and importers of energy resources (if country of origin has lower carbon tax than your country).
This is already done for income tax. You are taxed on your foreign income but you can deduce the tax you already paid to foreign country.
This could impact your exports but with the money from carbon tax you could lessen the tax burden on manufacturers of your exports or even finance them directly.
Still adding a large carbon tax directly at the source gives us pretty much the best bang-for-the-buck. It would have to be combined with deforestation taxes too otherwise you'll see countries like Brazil go into overdrive to export "green fuel".
In short, some people can afford to pay for climate change fixes, and some can't. Any solution will simply have to be progressive and have a fair, equal burden on everyone.
Maybe there's other ways to make it better for the people who can't afford it - a tax free allowance they can claim back or similar.
I'm still not sure if this is feasible across borders though. How can you stop carbon tax havens?
Unfortunately I can't imagine how diplomacy could achieve something like that, given the extremely uneven distribution of resource extraction industries. Despite that it wouldn't even hurt the big oil nations, considering that they would not have a lot of difficulties passing on the cost to their buyers (assuming full global enforcement). The biggest logical opponents would not be oil/gas states like Saudi Arabia or Russia but those whose only domestic geological energy sources is carbon-inefficient coal.
(Edit: cleared up some illegible grammar and editing clutter)