I've been printing for 3 years now...and in that time I've figured out that dark rooms are entirely overrated. Yes, emulsion reacts to light...but you really don't have to go to the extreme and prevent all light from entering your coating, drying, and storage area. You don't need to have a completely separate, highly restricted area in order to handle screens.
I do all of my coating right in my shop...I just shut the lights off. Sometimes there's sunlight pouring in the windows while I do it. Ambient light for a few minutes really does nothing. It's all good as long as you coat them quickly, don't let any DIRECT sunlight hit them, and get them into a fairly protected place for drying and storage (I just use a single storage shelf in my shop that has a piece fabric draped over and around it to block any direct exposure to light). After they dry, I just keep them on that shelf until I use them.
So...in summary...your options for coating and storing screens are likely much more abundant that you initially planned. Put forth reasonable effort in keeping them away from direct exposure to light sources for extended lengths of time and you'll be 100% fine!