I don't know for sure, since I've never used a pager in my life, but if you can send messages to pagers by using a normal phone by sending out extra numbers after the regular phone number, you could try dailing the extra long number directly with Device::Modem. You might possibly have to concoct the right AT command.
The protocol you may be looking for is TAP. This is a modem-to-modem protocol for sending pager messages, rather than dialing acoustical DTMF tones using a modem.
Check out sendpage at http://sendpage.cpoint.net/. The software is entirely written in Perl and may include what you're looking for.