I'll break down 3 lists of gear: Essentials, "Nice to have", and Luxuries...

To call coyotes, you really don't need that much, so the essentials list is pretty short and sweet.

The Nice to Have list is pretty much what I carry (not always all of it, mind you), shooting aids, comfort aids, and just handy stuff.

The Luxuries are things you don't really need, but sure are handy if you ever decide to splurge.

ESSENTIALS:

1. Rifle
2. Ammo
3. Calls
4. Accurate/up to date scouting maps
5. Camo - including gloves and facemask
6. Skinning knives

That's literally all you really NEED to call coyotes.

Nice to Have

1. Rangefinder
2. Binos (around your neck)
3. Padded seat/short stool (Cabelas Gobbler Lounger is FANTASTIC)
4. Coyote Drag (Send me a PM if you want one)
5. Shooting Sticks (LOVE Primos Shoot'n Stik Monopod)
6. Rubber gloves for skinning

These are items that really make your hunts or your shooting easier, and I'd recommend you have them, even though you can live without them.

LUXURY ITEMS:

1. Hitch mounted skinning winch and gambrel
2. Wind Meter
3. Ghillie Suit
4. High Seat (Truck or UTV mounted)
5. Electronic Calls

These aren't really necessary, but sure are sweet if you decide to splurge.

If you aren't good at judging wind direction, then pick up a small can of baby powder as part of your ESSENTIALS list.

I'm sure I'm forgetting a few things, but that's really all I can think of without looking through my pack.