First, install Internet Explorer 6 in Crossover via the Install Software menu.
To download the Java Runtime Environment installer, head to this page in a native web browser:
http://www.oracle.com/technetwork/java/javasebusiness/downloads/java-archive-downloads-javase5-419410.html
Click on the link for
Java SE Runtime Environment 5.0u22
Accept the license agreement, and then click the link for the "Windows Offline Installation" , towards the bottom of the table. You'll need an Oracle login to download the file - it's free to set up an account.
After downloading the "jre-1_5_0_22-windows-i586-p.exe", run this file using Crossover's "Run Command" tool inside your IE6 bottle and follow the prompts to install. When the installation is complete, IE6 will have the JRE installed.