What is needed for a G-matrix?
To construct the G-matrix you need additive genetic variances and covariances for all traits, so you normally need results from breeding experiments (e.g. phenotypic midparent-offspring data), that you can do parent-offspring regressions on. Don't know any good online sources but see Balding et al. 2007 p. 534ff for some info. I've seen methods that claim that the G-matrix can be estimated directly from phenotypic data from unrelated individuals (e.g. Zintzaras 2011) or from genomic info e.g. SNPs (Vattikuti et al. 2013), but are not familiar with these and do not know how reliable they are.

A clear background on using mixed models to estimate the G-matrix, including examples/tutorials, can be found in Wilson et al (2009).

Or did you have something else/something more specific in mind?