I have a rotten deck, but the previous owners painted it in a Hardrock-type covering making the screws impossible to find. How should I remove the boards with this complication? Do I cut it off with a reciprocating saw or will the coating on the deck just destroy the blades?
The deck screws are most assuredly made of steel which has iron in it. It should be very easy to find the screw locations using a magnet.
I have used these inexpensive type of magnetic nail/screw locators on walls and ceilings. I suspect they would work well on your deck as well.
(Picture Source: https://www.amazon.com/Stanley-47-400-Magnetic-Stud-Finder/dp/B0000BYD3K)
I use a rare earth magnet, small one, smaller than a dime. When pushing it along an area where screws may be, it will jump ahead to the screw and stop on top of it. Dig out the fist one to identify what type of bit it takes. Be certain you use the proper size. After that is established, you may be able to set the bit over the screw without digging it out and it may displace whatever is over the screw head and engage it well enough to draw out without clearing the head first of finish. It works sometimes, not all the time. You also must know when enough is enough for that technique so the head does not get stripped out so much the bit will not work at all after the screw head is cleared.
Maybe a little helpful hint for the magnet, figure a way to attach a string to the magnet so it will not fall in the gaps of the deck boards. Tape may work, or get a magnet with a hole for a screw in the center.
Not sure how rotten your rotten deck is, but I had a similar issue, and mine was so far gone that many boards could be removed by hand without removing the screws first. In some cases, I needed to use a pry-bar to get them started. This technique has the added benefit that you don't need to remove the screws, which can take a long time and forces you to work in uncomfortable positions.
Assuming you are not intending to save any of your rotten deck boards, that's what I would try first.
I'd use rare earth magnets to locate the screws.
Then I'd use a small hole saw and draw a depth line on it.
Use the hole saw around the screws so the boards are no longer held and can be pried up.
Once you've removed all the boards you are left with little pieces of deck and the screws on the surface of the joists. Take a recip saw with a metal cutting blade and then just run it along the surface of the joist to remove each of the circle pieces/screws. The only disadvantage here is that you end up with the screw shaft stuck in the joist, assuming you are re-using the joists for new decking you'll have to avoid the shafts - shouldn't be a huge deal.