So I have had a coon on a stretcher for the past seven days in 30-60 degree weather. The leather is stiff but it appears as if it's still "sweating". Do these things ever dry up?

Are you whiping the grease off?

while it dries?

?

I wipe mine every day or 2 during the drying process ,especially coons .Takes a while to get all the oil from the pelt

Well...You dont need to wipe them down (if they are fleshed right) some oil on the skin is ok.
My rule of thumb is when the nose is dry hard the coon is done.

Coons normally drip for quite a while. Mine quit when I take them off the boards. I never could see why you would wipe the natural oil from a coonhide. I would wipe myself plumb silly at this time. I have about 400 coon I just hung on stretchers, and if I went around wiping each one off, I would never do anything but wipe coon leather. The oil in a coonhide don't hurt a thing.

Yeah what Don said. Generally speaking I might, (MIGHT) wipe them down once during the process. What I will do is put my coon between sheets of cardboard for a day or two after I take them off the boards. This leeches out a lot of oil but by no means not all of it. Let's face it folks, fatty pelts such as coon and beaver will sweat until the tanning process is complete.

So how long is it ok to leave them on the wire stretchers? After removing them, how do you store them?

?

If you don't need the stetcher for other pelts, you can leave them on the stretcher until you are ready to sell or ship.

Once they are off the stretcher, hang them some place dry with good air circulation.

Thank you. Also, how do you know if you're using the correct size stretcher or perhaps could have gone up a size? Thank you.

I guess if the pelt completely fills up the wire stretcher and hangs over the end, you should have used a larger stretcher.

I throw mine in a bag of sawdust after fleshing. It sucks up the grease. Course I only do about 10 a year not 400 like Don.

That 400 is just a few days worth.
Livetrap your stretcher should probably be a no 4 or 5 wire stretcher if I remember wire strtcher sizes correct. I use all wood anymore and my stretchers are 7 3/8 to 7 1/2 in at the 32 in. mark. They stay at that size all the way to the base which is 48 in. from nose to base.
If you leave your pelts on wire untill you decide to sell them, make sure the wire is not getting any rust on it. The buyers don't like seeing rust on pelts.