From a magnet engineering perspective, the field-reversed configuration (FRC) fusion concept is commercially attractive due to its cylindrical configuration. Essentially, all large coils are solenoidal, which enables efficient structural support and relative ease of manufacturing, thereby enhancing commercial viability. A design option for future experimental FRC devices, which is currently under study, would require a large number of normal conducting electromagnets to produce the required magnetic field configuration for approximately 30 ms. One of the major challenges with such a system is a requirement to achieve a magnetic field profile which evolves with time and in which both eddy currents in major components and large plasma currents are also important magnetic field contributors. This paper describes contemplated magnetic configurations and the main types of coils and the coil design choices for each. It also discusses transient analysis performed to predict fields internal to a conductive vessel, while ramping magnetic fields, and accounting for vessel eddy current and plasma contributions. An estimate of harmonic errors due to displacement of the coils is provided. The dominant error field component is found to be from the dipole contribution. Harmonic errors from eddy currents due to plasma are briefly discussed.