Dear sir,
I am professional 2D animator, I have experience on animations for many different purposes, from a animated movie, music videos and more. As I understand, you are looking for 2D classic animation method, as tv cartoon shows, that mean frame by frame animation. My rate for this animation method is $29 usd per second of animation, this kind of animation requires a lot of work, that is why it's cost, which actually in my case is really low compared to what a studio will charge you.
Please take a look to my portfolio here on Freelancer where you can find samples of my animated works, just pay attention for the samples that says 2D classic animation and not the ones that says rig animation, which is a cheaper method ($13 usd per second): https://www.freelancer.com/u/GueloFilms
So contact me and let's talk about your project in details. I can assure you 100% satisfaction.
Regards
Guelo