Some additional detail on your use-cases and requirements might help, but possibly these two interfaces may be of interest:
CURRI - The Routing Rules Interface allows an application server to receive a notification on calls to certain specified DNs or DN translation patterns. The application can then respond with a directive for call handling, i.e. to block the call, play an announcement, redirect to another DN, etc.
https://developer.cisco.com/site/collaboration/call-control/curri/overview/
IPPS - IP Phone Services XML API provides for HTTP/XML based applications using the Cisco IP Phone LCD display. Applications can include interactive screens with menus, input fields, etc. and IPPS applications can be 'pushed' or popped up on phone screens via HTTP POST (see the CiscoIPPhoneExecute request)
https://developer.cisco.com/site/collaboration/endpoints/ip-phone-services/overview/