http://cats.brighterplanet.org/cats/how-should-i-clean-my-cats-teeth-without-hurting-him
If you're kitty has severe tartar issues, your vet probably recommended dental care. Check out the video? Maybe it will help you to eventually reduce the amount of cleaning needed? Of course, though, some cats just can't or shouldn't avoid the procedure.
But what I have done, right or wrong, with my own cats for 30 years is pick off the accumulated tarter with a fingernail. It
usually snaps clean off the tooth; and I make sure that any
tarter right at the gum line is picked off because that is where
the infections brew. I check the back molars carefully.
Sometimes rubbing dental toothpaste along gum line...it
works.
I've never had a cat who needed to have their teeth cleaned
in a vets office in over 30 years of cat ownership. Ever. I'm
convinced it is because I flick off the tarter before it has the
opportunity to create a environment where bacteria grows
and infects the gumline and eventually teeth roots.
Preventative measures are darn cost effective and easier on
the cats, IMHO
Good luck with your kitty.