You do not need to use GitHub and Travis CI. You can sign-up for Coverity account with just e-mail address and password, instead of with GitHub account, and you can add a project by filling out details form, instead of importing a GitHub project. Similarly, you can upload builds to Coverity Scan either manually or from your CI, instead of from Travis.
You have to Sign-up/Sign-in first at https://scan.coverity.com/users/sign_up, then you can open https://scan.coverity.com/download?tab=java (e.g. for Java) and get the software and instructions for doing the build.
If you want to use your own CI, you will get the info for doing both manual and automated build after adding a project at https://scan.coverity.com/projects/name-of-your-project/builds/new.
In essence, you can grab the build instrumentation tools either from the web site after logging-in, or by
wget https://scan.coverity.com/download/linux64 --post-data "token=<secret-token>&project=name-of-your-project" -O coverity_tool.tgz
(replace linux64 with your platform)
then you untar that and run the instrumented build
../cov-analysis-linux64-8.7.0/bin/cov-build --dir ../cov-int mvn -DskipTests=true package
finally tar the cov-int directory upload it with a HTTP POST request
curl --form token=<secret-token> \
--form email=<your-email> \
--form file=@tarball/file/location \
--form version="Version" \
--form description="Description" \
https://scan.coverity.com/builds?project=<name-of-your-project>