The next generation of wireless communications systems will employ new frequency bands such as those in the upper midband, millimeter-wave and sub-terahertz frequency bands. The high energy consumption of analog-to-digital converters resulting from their high resolution constituted a major limitation for future wireless communications systems, which will require low energy consumption and low-complexity devices at the transmitter and at the receiver. In this regard, we present a novel precoding method based on quality of service constraints for a multiuser multiple-input multiple-output downlink system with 1-bit quantization and oversampling. For this scenario, we consider the time-instance zero-crossing modulation, which conveys the information into the zero-crossings of the signals. Unlike prior works the proposed constraint is given in terms of the symbol error probability related to the minimum distance to the decision threshold and is included in the proposed optimization problem that is used in the design of the precoder. Simulation results illustrate the performance of the proposed precoding method evaluated under different parameters and scenarios.