KW is a guru in aftermarket suspensions, and the company has just released three new coilover kits for the BMW 4-Series Convertible.
The Variant 1 coilover kit comes preconfigured and cannot be adjusted. It still provides your 4-series with better stability, despite the extra weight of the retractable hardtop.
The Variant 2 model allows you to adjust the damping with 16 different settings, and if you go with the Variant 3 model you'll be able to adjust the compression with 12 settings as well.
Using KW coilovers kits will drop the height of your 4-series by somewhere around 40 - 65 millimeters on both axles. As of right now, there is no support for xDrive vehicles, but that should be taken care of in the near future.