This git repository will help you get up and running quickly with nexus running on tomcat on OpenShift.
Create an account at http://openshift.redhat.com/ , don't forget to create a namespace and install client tools as well.
Create a DIY application
rhc app create -a nexus -t diy-0.1
Grab this quickstart codes and make it working for you!
cd nexus
git remote add nexus git://github.com/shekhargulati/nexus.git
git pull -s recursive -X theirs nexus master
git push
That's it, you can now checkout your nexus at:
http://nexus-$yournamespace.rhcloud.com/nexus
The default nexus user is admin/admin123
Note: You can get the latest nexus code from github at https://github.com/sonatype/nexus-oss