Either use a heavy bullet and slow it down or pick up a box of FMJ, preferably not the military ball bullets with a cannelure. It would help if you loaded them down some also. If you shoot them fast and hit the shoulder, you will get secondary damage from frags. Though a cats hide is fairly tough, much more so that a fox or coyote basically. But beware if you get away from a destructive bullet it may not knock the cat down instantly.
There is another option. You can pick a super fragile light bullet and drive it as fast as you can. In the hopes that it will poke a hole in and disentegrate and not exit. That depends that it won't blow a huge hole as it enters and that it won't exit. Works a bunch better on larger coyotes but depending on the size of cats I suspect it could work there too.
If it were me I'd try the FMJ route. Went that way with a blunt nosed 55 from speer in my 22-250 on turkeys. Found that speed was still very destructive but once I downloaded to around 223 speeds or under it worked pretty good.
Get as close as you can, but utilize your skills as needed.