If the CS has not improved the coal there is an option under give a gift which is named "improve a resource".
It costs 200 or 250g and you can improve the resource you want in his territory. It helps if the CS has not improved strategic resources
If there is already a mine on top the coal resource, you can not improve it again. You have to wait until enough civilizations get to the same tech level, (I think atleast two civilizations must discover it) so that the CS also get the required tech.
This is unlike Oil. Whenever a CS has oil, you can buy the improvement and immediately get it, because the improvement is different from the current one. But in case of alloy, coal or even iron, you can not by another mine, if there already is a mine on top of it, your are doomed to wait.
But I usually use a great general to expand my territory, even though if I would steal territory from a CS, just to get that damn resource instantly.
Another way, which is slower and cost intensive is to atleast buy the third ring tiles being next to the resource. This will change the priority of border expansion, and if the resource is only in the fourth ring, it is very likely that your next expansion will be in that direction. If not, you could buy up all tiles where it would expand to, before the algorythm finally choses the forth ring coal tile. (You can always check the next border expansion, and the time until the expansion, in the city screen.)