Coil systems for producing the Straight Field Line Mirror field using axisymmetric and quadrupolar coils are calculated. Two applications are intended, a fusion-fission nuclear waste transmutation device and a small plasma deposition device. Position, size and current for the axisymmetric coils are optimized as well as radial profile and current for the quadrupolar coils for the two applications. Calculations show that such a coil system can produce the Straight Field Line Mirror field for long-thin mirrors with moderate mirror ratio, but some other coil configuration needs to be found for mirrors where the coils cannot reside close to the plasma edge. In this work, the material science experiment mirror can be produced with about 1% error but the fusion-fission device field has not at this moment been reproduced with acceptable errors.