Yeah, if this is hard to access and not going to be moved, you really want to use sand or gravel or a mix of the two. NOT anything organic.
You'll want at least 4-6" minimum. If there is plenty of headspace then you may be able to just chuck that in there and accept the 'higher floor'.
Otherwise, you would have to raise the whole coop up. As long as it is not actually anchored into the ground by sunken posts or anything like that, you can move it by jacking up one end at a time. BE CAREFUL
You can put down a piece of plywood or a large paver to set the jack on so it doesn't sink into the ground (you can use your car jack), or if you have a coupla strong friends, see if you can find a way to get a couple pieces of strong wood in there for leverage and have them do it. Block one end up, then the other. Now put a row of cinderblocks or concrete rubble or whatever around the edge to make a firm LEVEL sill that you can lower the coop back down onto. Put gravel in, and you should be good to go.
Good luck,
Pat
You'll want at least 4-6" minimum. If there is plenty of headspace then you may be able to just chuck that in there and accept the 'higher floor'.
Otherwise, you would have to raise the whole coop up. As long as it is not actually anchored into the ground by sunken posts or anything like that, you can move it by jacking up one end at a time. BE CAREFUL

Good luck,
Pat