Installing ionCube on a VPS isn't any different to installing it on a dedicated server.
ionCube doesn't need to be installed to run, most servers support 'ionCube runtime loading' which allows the loaders to be run as and when they are needed, without needing to install them or modify any files.
For best performance though, it's a good idea to add the entry to the php.ini for them.
To see if this is already the case, visit any phpinfo page on the server and look in the box just below the first main table. It will say something like:
"This program makes use of the Zend Scripting Language Engine:
Zend Engine v1.3.0, Copyright (c) 1998-2004 Zend Technologies with Zend Extension Manager v1.0.10, Copyright (c) 2003-2006, by Zend Technologies".
If in that same part you see a mention of the ionCube loaders ("ionCube PHP Loader v3.1.22, Copyright (c) 2002-2006, by ionCube Ltd."), then they are already installed and you don't need to do anything