For my 1-8" twist 22-250 and 1-8" twist 223AI I use the Barnes 55 gr MPG Lead Free bullets and they do a decent job on coyotes.
I have seen seven coyotes shot with the Hornady 35 gr NTX Lead Free Varmint bullets out of a 223 Rem and a 22-250 and all of those coyotes died quickly.
This last season I used my 243 Win with 55 gr Nosler BT Varmint Lead Free bullets. This bullet was very accurate but at times really did some damage.
The Barnes 62 gr 243 Cal Varmint Grenades also do a decent job on coyotes.
I don't use any of the GMX, E-Tip, TSX or TTSX bullets for hunting coyotes.
I have seen quite a few coyotes shot with TSX and TTSX bullets in 243 Cal, 260 Rem, 300 WSM and 30-06 and all of those coyotes died quickly without much fur damage. All of these coyotes were shot while deer hunting.
The 50 gr TTSX Barnes bullet should open up on a coyote. Unless you hit bone it would probable be a small entrance and exit hole.