I know you can go to your voice mail and enter in your password. Then select the option "send a message".  You can send a voice mail to another verizon customer. Their phone won't ring at all. The voice mail will just appear on their phone.

if their not a verizon customer then you could use the Spoof feature. Although using this feature you'll still have to call the person, but you can make another phone nubmber appear on their caller ID.