The MiniGRAIL is one of the three similar spherical gravitational wave detectors that are currently being developed. The detector has a resonant frequency of about 3 kHz and will be operated at 20 mK. The ultimate goal is to use a readout system consisting of six transducers coupled to nearly quantum limited two-stage SQUIDs. The two-stage SQUIDs are based on double relaxation oscillation SQUIDs, which enables a direct voltage readout scheme. We have developed nonintegrated two-stage SQUIDs and experimentally verified the proper operation of the system coupled to a capacitive transducer. Based on the results that were achieved, integrated two-stage SQUIDs were designed. Special attention has been paid to the sensor SQUID, the back action of the SQUID and the feedback scheme that is used for linearizing the SQUID output.