They appear to have an API for Manual data logging. Specifically, they mention Logging internal events:
Logging data from an internal script
Clicky lets you log data from an internal script, such as PHP, ASP, Perl, etc. Other services don't offer this feature because they don't document their incoming "API", and they only verify incoming data from the referrer. Clicky is different.
It seems to be really made for your backend webserver scripts to also contribute user data, but I'm pretty sure you could make the web API calls from whatever language you'd like, including a WinForms script. Not really what it's made for, but hey, why not? Just issue a GET request with the URL-encoded parameters:
How to talk to our tracking servers
The page you want to talk to is at http://in.getclicky.com/in.php
. This is the same script that our tracking code talks to. You just need to send the right parameters, and we'll log it.
So you'll need to port their example PHP Script to C# and you'll be good to go.