A promising approach to reduce energy consumption is to consider coarse quantization at the receiver. In this study, we investigate novel precoding techniques in space and time for bandlimited multiuser MIMO downlink channels with 1-bit quantization and oversampling at the receiver, considering zero-crossing modulation. The proposed time-instance zero-crossing modulation conveys the information into the time-instances of zero-crossings. Two design criteria for time-instance zero-crossing modulation are investigated, namely, the minimum distance to the decision threshold and the mean-square error between the received and the desired signal. The maximization of the minimum distance to the decision threshold can be formulated as a quadratically constraint quadratic program. As an alternative, an equivalent problem is formulated based on power minimization, which reduces computational complexity. Moreover, another method is implemented where the information is conveyed into the time-instances of zero-crossings using waveform segments. Departing from the conventional mean-square error based technique, a more sophisticated algorithm is developed, which implies active constellation extension to improve the performance at high SNR. The extended problem is solved with two approaches: by formulating the problem as a second-order cone program and by considering an alternating optimization algorithm. Another method based on the gradient descent algorithm is implemented with the mean-square error technique to reduce computational complexity further. Besides, a lower bound on the spectral efficiency is obtained. Numerical results show that the proposed time-instance zero-crossing precoding methods significantly improve the bit error rate compared to the state-of-the-art methods. Finally, the maximization of the minimum distance to the decision threshold and the mean-square error based precoding techniques are evaluated considering a frequency-selective millimeter wave channel. Numerical results show that both precoding techniques respond well to the frequency selectivity of the channel.