Does a public database exist that contains this information? I'm trying to make a simple gene annotation program that will let me input a DNA sequence and then optimize it based on one of these tables using the E. coli preferences, for example.
Try the Codon Usage Database at Kazusa. You can search by organism. The database contains 35,799 organisms and compiled from 3,027,973 complete protein coding genes (CDS's), but last updated in 2007.
Plenty of softwares doing that kind of functionality. A 2007 open access review lists >30 such softwares http://www.ncbi.nlm.nih.gov/pubmed/17882154. However, No correlation between 'most common' codon and recombinant protein expression yield. http://www.ncbi.nlm.nih.gov/pubmed/21102527. Thus, those >30 softwares are pointless.