If you cannot do the tire test to get the tire force database under different conditions, you may use the two methods below.
First, you may use Magic Formula tire model to generate the tire forces under different road conditions and vertical loads. Specify a set of fixed points for road conditions vertical load and steering angle. Do simulations and save all the tire forces in a database. Then you can use lookup table to determine the tire force for a specific case.
Another way is, you can use the tire data in CarSim if you have this software.