There are day rates at the Air Rooms by Premium Traveller inside Terminal 4 but I doubt they could be any cheaper than a night rate at a nearby airport hotel you can reach by shuttle.
You could also pay for lounge access in one of the contract lounges for 26€ in Terminals 1-3 which is great value. I took a nap on the sofa there once. Iberia's lounge in T4 also has a sleeping room which is very nice.
In Spain day rates also apply to "love hotels" and there are several of those in the area but I am not sure that is what you were looking for.
In any event, you'd be better off reserving this kind of thing closer to the date given the travel situation.