There is a nice paper of Cabibbo and Gatto from 1961 about e+e- going to pions
and other states. For the historical context of this work cf. e.g. this nice article.
Cabibbo and Gatto provide results for many interesting tree level calculations
(that are still relevant for nuclear physics) that are done without really relying on Feynman diagrams.
Using FeynCalc one can write down the amplitudes by hand (i.e. without using FeynArts) and then
show how to calculate x-sections and decay rates. That would make a lot of nice examples.
The attachment contains a rough sketch partially reproducing one of the first results in the paper.
CabbiboGato.zip