Yes, the Sony ICF-C1iPMK2 docking station is compatible with the CoolStream Duo. You can plug the Duo into the 30-pin connector of this docking station and stream music or podcasts from your phone, tablet, or laptop. The CoolStream Duo works with ALL iPhones and All Android phones.
The CoolStream Duo turns older docking stations like this classic from Sony into Bluetooth speakers. The 30-pin iPod connector powers the Duo and is also the audio jack for the music coming from the paired phone. You can check the model number on the bottom of the Sony docking station.
For more information about compatible (and non-compatible) docking stations, check out the Docking Station Compatibility page.