In my opinion TSS #4 shot would make her a much better coyote load for a 20 ga gun. A Modified Choke or a I/C choke will probably be plenty tight enough with TSS shot. For shooting coyotes at 40 yards and less the I/C choke maybe the better choice for using 20 ga TSS loads.
For my 12 ga TSS coyote loads I use a Mod or an Imp/Mod choke. Since TSS #3 shot and #4 shot give more than enough penetration to kill coyotes, I like them better than TSS #2 shot because of the much higher pellet counts per shell.
From KPY Shotshell Ballistics
1 ounce of TSS #4 shot at 1250 fps has about 83 pellets and gets 3.70" of gel penetration at 76 yards.
1-1/2 ounce of lead BB shot at 1350 fps has about 77 pellets and gets 3.70" of gel penetration at 48.8 yards.
1-1/2 ounce of TSS #2 shot at 1250 fps has about 81 pellets and gets 3.70" of gel penetration at 111.8 yards.
The 1 oz load of TSS #4 shot has 2 more pellets than the 1-1/2 oz load of TSS #2 shot and the 1 oz load will have WAY LESS recoil than the 1-1/2 oz load has.
Look at how the 1250 fps TSS 1 oz load compares to the 1350 fps 1-1/2 oz load of lead BB shot.