The DSC computer basically compares each tire's actual revolutions per second and the car's indicated speed against a formula. The formula is programmed in the computer for a specific tire size. Your tire size is too small in diameter, and the computer thinks that ALL of your tires are losing traction so DSC kicks in.
www.1010tires.com has a calculator that tells you what will work or won't work. They say you should be within 3% of the factory diameter. You are 4.5% smaller. It seems like not much, but the computer is not forgiving! Common thought is that the computer CANNOT be recalibrated. Actually, it almost certainly COULD be recalibrated, but that would be a HUGE legal liability for BMW to let people recalibrate a safety system.
205/50/15 is the closest size that will be under 3%, but I'll bet they won't fit your rims.
Stock Tire - 185/60R15 New Tire - 195/50R15
Section Width:7.28 in185 mm -/- Section Width:7.67 in195 mm
Rim Diameter:15 in381 mm -/- RimDiameter:15 in381 mm
Rim Width Range:5 - 6.5 in -/- Rim Width Range:5.5 - 7 in
Overall Diameter:23.74 in602.99 mm -/- Overall Diameter:22.67 in575.81 mm
Sidewall Height:4.37 in110.99 mm -/- Sidewall Height:3.83 in97.282 mm
Radius:11.87 in301.49 mm -/- Radius:11.33 in287.78 mm
Circumference:74.58 in1894.3 mm -/- Circumference:71.21 in1808.7 mm
Revs per Mile:876.1 -/- Revs per Mile:917.5
Actual Speed:60 mph100 km/h -/- Speedometer:62.8 mph104. km/h
Speedometer Difference: 4.725% too fast
Diameter Difference: -
Diameter Difference: 4.51%