Go into WHM. Under DNS functions, select "Edit DNS Zone".
It will bring up a list of domains, and subdomains.
First select the domain it's currently pointing to. Edit that domains A record to point to the IP it's meant to go to - such as 192.168.1.254/~example.
Note: the addon domain will have a directory, if you only have 1 dedicated IP for said account, it will need to point to the dedicated IP with the directory of the addon domain.
Example: youriphere/addon/domain/directory/
Then select the domain it's meant to point to. Then edit that domains A record to point to the IP in question.
For a list of DNS record types and their functions see this link:
http://en.wikipedia.org/wiki/List_of_DNS_record_types
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It can be done under cPanel. Just click on "Simple DNS Zone Editor." Delete the A Record for the domain it's currently pointing to. You'll need to replace the A Record of the new addon domain with the IP address "youriphere/addon/domain/directory/"