Yes, there is a formula for calculating the wheel rate required to achieve a certain ride frequency: f = (1/(2pi))v(K/M) where f = frequency, K = wheel rate, M = sprung corner weight (corner weight minus unsprung weight). The question is what ride frequency is appropriate for a sports car?
Luxury cars typically have ride frequencies of 1.0 to 1.2 Hz, regular cars 1.2 to 1.5 Hz, high performance cars 1.5 to 1.7 Hz, street/track cars up to 2.5 Hz, race cars 2.5 to 4+ Hz depending on how much downforce they produce. Of course, the ride gets progressively harsher and stiffer as you increase the ride frequency – try driving an ALMS or IndyCar to work someday! Once you choose a frequency, and determine the wheel rate, you calculate the spring rate by using the square of the motion ratio between the wheel and the spring.
For example, let’s say you have a 3100 lb BMW M3 street/track car with 50/50 front/rear weight distribution and want a 2.0 Hz ride frequency: the total weight with driver and some fuel is 3300 lbs, so the corner weight is 825 lbs, the unsprung weight per corner is 75 lbs, so the sprung weight per corner is 750 lbs; using the formula above the wheel rate =
306 lbs/in, and with a front spring to wheel motion ratio of 0.91 the spring rate = 370 lbs/in.
Now, for the damping, you need to decide how critically damped you want the system. Luxury cars have less critical damping than sports cars which have less critical damping than race cars. 100% critical damping = 2 v(K*M) with the same inputs as above.
Back to the M3 example lets say you want 70% critical damping: using the formula, 100% critical damping = 49 lbs/in/sec, so 70% = 34 lbs/in/sec, and with a front damper to wheel motion ratio of 0.91 the damping force required = 41 lbs/in/sec. Of course this is a simple example and there are lots of opinions and experience in the field of vehicle dynamics about the level of rebound versus compression damping, low speed versus high speed damping, position sensitive damping, frequency dependent damping, and g-level sensitive damping which you can spend an entire career optimizing if you work in vehicle development.