Our current Coverity Scan builds occur multiple times per week out of buildbot. There is a new integration that allows Coverity Scan to link to a GitHub repository, as well as one that allows Travis CI to submit builds to Coverity Scan.
Drawbacks include Coverity Scan's lack of accommodation for branches; its defect tracking for new and resolved defects implicitly assumes a single branch of development. There is a maximum rate of build submissions per week, so monitoring the master branch isn't appropriate. Coverity's recommended approach is to use a dedicated "coverity_scan" branch, but that would require manual developer work to update given our version control current setup.
Greg suggests a combination of our current setup with the Travis CI/Coverity integration. We would need to make an exception to allow force pushes to the "coverity_scan" branch. It would also help to use a newer buildbot version that can avoid redundant builds of unchanged sources.