This information is for TaskPaper 2 which is old and outdated. TaskPaper 3 is the current version of TaskPaper. For TaskPaper 3 support please visit the support forums.
To create a new task at the end of document:
tell application "TaskPaper"
tell front document
make new entry with properties {name:"- my new task"}
end tell
end tell
To create a new task in an existing project:
tell application "TaskPaper"
tell front document
tell project named "Inbox"
make new entry with properties {name:"- my new task"}
end tell
end tell
end tell