Your wish to preserve the rug is understandable......but risky. More important is quickly and humanely dispatching the cat. You certainly don't want to wound it and have it escape. Someone else might end up picking up that tab.
The recommendations for FMJ bullets that wont expand much demand a heart-lung hit. If the range is that close, a head shot should be available. Try to make a sure kill more of a priority that rug preservation.
That said, almost any reasonable, accurate big game bullet will work on a close range head shot. If you are going body, forget the rug issue and use a quick opening soft-point like a SuperX Power-Point, or a Federal Fusion. Shooting up into a tree may create difficult angles to the vitals and you just don't want to pencil a bullet through the guts and have kitty charge away.
Many years ago, I lived in a Mountain village here in Colorado. A mountain lion had been dining on pets for about a month. I caught him one evening enjoying the neighbors German Sheppard and he had no intention of abandoning his meal. My first 30-30 shot was too far back. I had to snap off a second shot into the haunches to slow him....another to the abdomen to slow him more, and finally a lunger stopped him. Granted, with a scope instead of my open sights, the first one might have done the job. The point is, them big kitties is hard to kill!!
