Tarp?

Sounds good. At least worth a try if the chickens can't scratch it apart into shreds and not each the parts they tear up.

Check for remnant linoleum at a flooring store or Lowes, we found the last of a roll, 6ft x 17-ish ft for $12. Way cheaper than the pre-cut small sections they sell for $25-ish. Since both sides of our coop are 5x7, it worked great!

We didn't paint the floor, so far so good.

We cut the corners for a neat edge up the sides. On the duck side where it's prone to dampness, it's been working really well.

The tarp isn't going to age well with them scratching in it, unless you really pile in the bedding from the start. Up the sides where it's exposed, they may peck and yank on it. They might not.

When you go to shovel it out, it'll will be a pain with the tarp unless you get it most of the way empty, then pull the whole thing out. Not sure how often you'd have to replace something like that.

Also I'm not sure what grade the plastic is, and how having composting material on top of it would affect it. You'd have to check periodically to see how it was holding up.

Are you talking about a REAL canvas tarp?, Or one of those blue plastic things?  The chickens will shred one of those blue tarps, and you will be hauling out the scraps of it with the rest of the bedding.  Since your coop is new, I would recommend  a product from Lowes,  Blackjack#57. It's a rubberized roof coat product that comes in a 5gal can.  I put it down on my coop's floor 2 yrs ago, and it looks as good as the day I put it down.  It totally seals all floor gaps, plus the gap where the walls meet the floor.  It becomes a permanent part of the floor.  Nothing can get under it and touch the wood floor.  It does not get brittle and crack apart like linolium.   It's not easily damaged like vinyl. I think it's the easiest to install.  You just pour out a big glob on the floor and push it around with a roller.  IMO,  It's the BEST coop floor protector you can get.

Jack 

4 mil(or greater) plastic would be cheaper and last longer than a tarp and can be stapled down and then ripped up when needed.  Tarp has texture that will hold the particles and can be caught by the nails of scratching hens, whereas the heavy plastic may puncture but it won't tear, it won't hold particles and it won't be easy to scratch up due to the thickness and slickness. 

I like the sound of this coating a lot better than either option. 

I have a tarp in place in part of my coop . It works great. after awhile my husband or just me  pick up all 4 corners and move to the compost pile . Works great.