Thanks for all the info. I'd have to look at a 7" Kindle Fire but it does sound like it might be too small although if they're made for reading it might be ok. I'm dealing with a lot of paragraphs that are read separately so only seeing 1/3 of a page at a time would be ok for the most part.
I didn't want to get involved with a teleprompter although in many ways that would be a perfect solution if it were completely quiet and were $200

I can't put a laptop in the booth because they do make some noise albeit not as much as a desktop. I thought a tablet would be a very elegant solution since I believe they are completely quiet, right?
My search started with the Kindle because of price. Since I'd only be using it to replace printing of paper scripts it didn't make sense to spend 3-6 hundred on one of the other fancier tablets.
If you're talking scripts that are basically paragraphs. . .as opposed to a lot of stage direction and character switching like you'd have with the script, say, for a play, a regular Kindle might do it for you. If it's in Word, you could easily format it so that when converted to MOBI (the native Kindle format) it works just fine and they can change the size of the font to their liking.
It's not completely silent, necessarily, some find the button click is audible but most don't notice it at all. A touch screen device, of course, would not even have that.
Fire is also touch screen as a small tablet. . .but it's not eInk so would be a different reading experience. It would still take a MOBI format file -- which allows for print size adjustment -- as well as other formats depending on the additional apps installed.
If it was me, I'd try the eInk kindles first. . .they're much cheaper. If they don't work you can return them within 30 days for a full refund (less return shipping). If you can get a template worked out to put your scripts in, you might even find that some people already HAVE Kindles. If they do, it would technically be possible to just send the scripts to them directly.
You might ask in the Writer's Cafe area for some guidelines on formatting for the Kindle . . .