Download java from http://www.sun.com and put the package in /usr/local/bin. Make the file executable and accept the license terms and conditions. Then find the file libjavaplugin_oji.so and create a symlink in /usr/lib/mozilla/plugins/. Then open Seamonkey and choose:
Tools>Add on manager>plug-in
And activate java.
If this procedure does not work then you have to make a symlink to libnpjp2.so. For example if you have installed java 1.6.0_31 in /usr/bin do like so:
ln -s /usr/bin/jre1.6.0_31/lib/i386/libnpjp2.so /usr/lib/mozilla/plugin/
Please make sure to install the latest java environment otherwise Seamonkey does not recognize the installed version.