Currently the weather feature in OpenSprinkler firmware requires WUnderground API. If you can set up your weather station as a Wunderground weather station, then you can use its data through the weather algorithm.
Another way would be to involve another web server (it can be a Raspberry Pi), which gets information from your weather station, and sends an HTTP request to OpenSprinkler to change its rain status (you can use the rain delay API). It’s possible to modify the OpenSprinkler firmware to obtain this information from your weather station directly (without having to use another web server), but it’s often easier to write a Python script on Raspberry Pi than to modify the OpenSprinkler firmware.