first of all sniff the program or take the link of service api to reproduse the request
second it's very simple
zennoposter handle auth headers in the additional field (where you type useragent string)
mainly it has two types:
like plain string
Basic ZWx1c3VhcmlvOnlsYWNsYXZl
Basic login:password
or in b64 encoding like
Authorization: Basic YWNjX2ExN2FkNGFkNzNmZTYyNTpmODgxMWEyY2MzYTAwNzI3MDU5YjY5YzIxOTA2ODgzNg==