Count me in with the “keep it around to hang up when they come over, then stash under a bed somewhere”.
Or make “changes” to it, to make it more kitsch. A bow on the cougar’s head, for example, or the Death Star hanging in the sky.
swap it for a velvet painting of elvis
Don’t be a wuss. Nobody appreciates that.
Be honest.
Sometimes the truth will set you free. Tell your friend the painting just doesn’t fit the overall theme of your decor and given your appreciation of her thoughtfulness that you must return the gift to her.
Take control of your life. Sure, it might take your friend aback somewhat but she’ll get over it real quick and Bob’s your uncle.
And for sure you will never get another painting from her.
I’m a Buddhist and collect stuff like that. If you’re willing to get rid of it, I’ll at least take a look. Maybe it’s only ugly if you’re not into that kind of thing.
It’s my understanding that a cougar painting is never unwelcome or unwanted, so the only answer is to hang it in the shitter–right above the throne.
Those go for a lot of money these days. So that would actually be a hell of a trade.
Tell her your neighbor showed up to show off his new hunting rifle, was startled by the picture of a cougar on the mantle, and shot it.
I LOVE both of those ideas!
Sorry if this has already been suggested but the only solution as I see it is to burn your house down along with the painting inside. And hope that she just doesn’t get you another copy of the painting!
say that your cat attacked it
Rat-tat-tat-a-tat!
[spoiler]Chanson d’amour,
ra da da da da,
play encore Here in my heart,
ra da da da da,
more and more[/spoiler]
pick a charity
raffle tickets for a minimum donation to said charity
award painting to random donor
can’t speak for the rest of the dope, but I’d gladly donate for a chance to win this painting; it instantly becomes a conversation piece.
Bedazzle it.
Great answer! 
This has the whole cast of “Are You Being Served” singing in my head. And I don’t even rememebr the episode!?! 
I may just have to start giving my siblings horribly kitschy artwork for gifts and tell them that I found the perfect gift for them. Then I get to imagine the conversations that go on at home as they decide what to do with them. The best part will be wondering what sitcom hijinx they are going through whenever we come to visit. I’m a bad brother.
The last episode! Bert Spooner becomes a hit.
I had to look it up because you put that damned song into my head.
It was also the plot of a Frasier. Martin Crane bought Frasier a hideous huge Spanish bullfight oil painting - one of those garish splashy neon colored ones - and Frasier felt obligated to hang it over his fireplace.
When he finally told his dad that he hated it, Martin broke down crying!
Do this!!!
Tell them it was so wild and majestic that you couldn’t keep it penned up inside some suburban jail, pinned to the wall. You HAD TO set it free. So that it could roam in nature (down at the quarry).
If it comes back, then it was meant to be.