I have once used 2 days old coated papers, they work. That does not mean they are ideal to use. But in a very humid areas, highlights of the print would be fogged after a day. (I have also seen a week old paper with fungi on it.)
IMO, stored paper will behave differently then fresh coated paper, for consistency it is wiser to coat and use with in few hours.
I used the "new" formula kit from (I think) the Formulary. I used a sheet or two within a few days of coating, but had some that sat around for over a year (maybe multiple years) and they were ok. I wasn't doing anything very detailed, not was I looking for high end results. But I did get prints out of them even a looong time after coating.
Next day should be OK. Or you can try a hair dryer but if you do make sure the paper is completely dry or you'll ruin your negative. Otherwise do what I do, put a piece of mylar between the negative and the paper.
Keeping qualities really depends on the paper. Paper is the bane of Alternative Processes. I've coated cyanotype I could use a month later on one paper, and some I could not use the next day on others.
On dry coated paper yellow is great, green OK, as long as the surface hasn't truned blue or blue/green you should be fine.
The best advice is get in the darkroom and trycoating your paper and see what happens.
Joe
And keep track of what paper each sheet is so you can replicate your results. Date coated, brand and type of paper, formulation of cyanotype written on the back in pencil is something I wish I'd done.
i have used some old coated paper that was nothing fancy, butcher paper ...
it was over a year old ... it looked kind of weird before i exposed it, but when it was done
it gave the most beautiful greens and yellows and blues ...
YMMV
You could go for a 2-step cyanotype - coat the paper with the ferric ammonium citrate and let it dry, store it, expose it, and then develop it in the potassium ferricyanide. It would probably fog less in humid environments (depending on how the paper reacts to the FAC). Haven't tried it, but it'll also give you 2-3 stops improvement on exposure time.