Need a way to delay power off on 24vdc circuit

I have a 24vdc coil (1.8 w) that I am thinking of putting a capacitor in series with to cause a delay of about 1-2 seconds. First, do you think this would work? Second, if it would, what size would I need to maintain 24v for 1-2 seconds.
This idea might be in far fetched, but I thought I would give it a try. I have a P/E with a 100ma output I am firing the solenoid, but want a 1-2 sec delay for the P/E to clear before I de-energize the coil. I am trying to keep it simple and cheap because I am installing roughly 400 of these.

Any advice would be greatly appreciated...

What is a a P/E?

It would take a capacitor in PARALLEL with the coil to keep the relay power after the input power goes away. The resistance of the coil is R = e^2/P = 24*24/1.8 = 320Ω, so it would take C = 2/R = 7000uF capacitor to hold in the coil for ~2 sec, which is a huge capacitor. You would also have to consider how long it would take to charge that capacitor from the P/E output, whatever it is? It might be necessary to limit the current into the capacitor, too, because when the P/E switches on, that capacitor is going to look like a dead short.

Offhand, I'd say that this is impractical...

I see .....

Thanks for the insight. It was a shot in the dark. I was hoping to find a cheap tweek on my project, but it will still work as designed with out the delay... I was just trying to same some cycles on the solenoid.

Sorry about the P/E. That is a photo eye (difused). I am using it to sense cases going by on a conveyor.