I'm on my third generation, but when the second happened and I had all the gotchi points from hitting it big as the band, I starting to buy any new non-food item that happened to cross my path in the Shop. Using these items is like playing with your Tama's, and a couple of the best ones are Slide and Jeans. While this lowers stress, some of the items - like the costumes, Pencil, and Make-up - are one time use only while others like the Mirror and the Slide and Jeans are permanent, so don't buy two infinite items, that's a waste.
For me, I normally keep my Tama's stress between 0 and 10 by checking every little while or so, or right before class - I'm in college - I fill all his hearts and stress to zero. That way, if you can't get to him in class until break or something, he's got it good and can wait the better part of the hour.
Also, anytime that you catch your Tama practicing without being told, Praise him/her. This lowers the stress level, and also makes them happier and enjoy the instrument more, or so I've found.
~Kikitchi~Kitty