There is a standardized protocol for sending alphanumeric pages known as "TAP" (originally known as "IXO"). Writing a utility from scratch using a shell script ought to be plausible, even if it's less effective than using existing software.
Were I to pick up an alphanumeric pager, this would be a useful resource...
The fax management system Hylafax contains a pager "gateway;" it can be used to either directly send faxes, or to route other messages to it.
A venerable general purpose serial/network communications client that runs on many, many, many platforms, and can also manage alphanumeric and other pagers.