This question gets posed pretty often. If the CS has already mined the tile, it won't provide the strategic resource (coal, aluminum or uranium) until the CS has researched that tech. If, however, the tile is not improved you can gift 200 gold to improve the tile. ("You want these dirty rocks? Can't imagine why, but OK.")
It used to be 'Scientific Theory' - in BNW it's 'Industrialization'.
To the OP - it doesn't matter what you yourself have researched - the City State itseff has to research 'Industrialization' before it can gift you the coal. City States operate exactly the same as any other Civ (apart from the fact that they can't settle new cities) - this includes doing their own research and gaining the benefits - and resources - that come with new technology.
On the upside, if a CS researches a tech that reveals a resource before you research that tech yourself, they will still gift it to you if you are allied with them AND you will be able to use it too! This is particularly useful when a Civ researches 'Biology' before you do and you have researched 'Flight' as it means that you'll be able to build planes without even knowing what oil is!
Like the other posters have said, for resources it's the CS that needs to have researched said tech. So you'll have to search for other CSs that also have coal, but that's situated not on a hill. (Since City States most likely will have any hills mined already) Then once you find it, gift them the resource.
This question gets posed pretty often. If the CS has already mined the tile, it won't provide the strategic resource (coal, aluminum or uranium) until the CS has researched that tech. If, however, the tile is not improved you can gift 200 gold to improve the tile. ("You want these dirty rocks? Can't imagine why, but OK.")
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