I like a short chain too. All of my coyote traps have a quick link around the trap base with the threaded sleeve of the quick link spot welded shut, then a 4-way universal swivel, then no more than 3" of welded kinkless chain, then another universal swivel. I don't have more than 10" of chain/swivels on any of my predator traps. For anchors I use either 20" length of 3/32" cable with an earth anchor, or I attach a butterfly style double stake swivel and cross stake with 24" stakes made from 1/2" rebar and washers welded just below the top 1/2" stake end.
Probably more overkill for coyotes than needed, but seems to help keep the two-legged predators from walking off with my traps anyway.
The short length of chain really seems to keep the coyote from getting a decent lunge. They can really build up some momentum on a long chain and then they hit the end of the chain with much more gusto.
Best combo I've found that works for me anyway is a lot of swivels and a very short overall chain length, with a stout anchoring system. I also run a lot of dirt sets for coons, using #11s at double dirtholes loaded with fish and red fox gland lure. I've held a lot of coyotes in those little #11s too, and even a couple of cats. Yes, that's way too small a trap to use specifically for either animal, but I also don't think any of them would have been there waiting for me the next day if I had used long chains either.
The only time I've ever ran long chains on my traps was when I was using some grapples on coon sets in a dry creek bed. Those were of course very long chains (about 7') made from odds and ends lengths cut from the original longer chains on my new predator traps.