You can create your own custom online forms using a form generator, like phpFormGenerator (found in Fantastico).
NOTE: There is a known issue with the permissions of files created by phpFormGenerator. When creating a new form some files will have permission of 777, which will lead to errors on our shared and reseller servers. The files' permissions can be changed via the cPanel File Manager, SSH, or we can correct these for you, however please note that this will need to be done after each new form creation. Please see the following article for more information: How to Change Permissions / CHMOD-of-a-File.
Another known issue with phpFormGenerator is that it does not include password protection by default, which means that a new installation of the script is accessible to anyone. Because of this we would strongly urge you to set up password protection for the directory immediately after installing this software. The following article gives instructions on how to set this up through cPanel: Password Protect Directories.