Any suggestions for catching one (ie, traps)?
I use a raccoon size Havahart live trap with a single door. I usually place a can of half open undrained tuna in the back of the trap then cover it with cardboard or wood. This helps collect the scent around the trap then as the wind gets to it it drifts out and is a great bait for cats and coons. The trap remains set up in a single location near my garbage cans. I don't seem to have any possum here in my neck of the woods so I don't catch any of them. I have however trapped over a dozen cats in the last couple of weeks and a few coons too. It seems the feral cats outnumber the coons here.
Every varmint that has gone into that trap has never made it out of the trap alive. They all enter the trap and leave by way of a .22short bullet to the top of the head from my single six. I use a .22short so I don't get overpenetration - I don't want to put any bullet holes in the catch plate of my trap.
Anyway cats and coons can't seem to resist the smell of tuna going bad. Try it and see what it does for you.
I have adopted two West Highland White Terriers from a rescue organization here in Southern California. In the last 18 months the have killed 2 rats, 5 mice and 9 oppossum. They each weigh about 18 pounds. If the cats would come down off the fence, they would be history, too....
Two 18lb Westies would have difficulty with a healthy mature feral cat. Those things are lean, mean and agile killing machines. I've seen a single feral cat take on and chase off full grown german shepherds, pit bulls and even a small pack (4 dogs) of jack russels terriers - not the same cat but I've seen those incidents with different cats. Be careful with your wish for a cat to climb into your yard. While you may end up with a dead cat to dispose of you may also end up with one or two heavily wounded dogs to care for too.