This work considers the precoding problem in massive multiuser multiple-input multiple-output (MU-MIMO) systems equipped with low-resolution digital-to-analog converters (DACs). In previous literature on this topic, it is commonly assumed that the channel state information (CSI) is perfectly known. However, in practical applications the CSI is inevitably contaminated by noise. In this paper, we propose, for the first time, an eigen-inference (EI) precoding scheme to improve the error performance of the coarsely quantized massive MU-MIMO systems under imperfect CSI, which is mathematically modeled by a sum of two rectangular random matrices (RRMs). Instead of performing analysis based on the RRM, using Girko's Hermitization trick, the proposed method leverages the block random matrix theory by augmenting the RRM into a block symmetric channel matrix (BSCA). Specially, we derive the empirical distribution of the eigenvalues of the BSCA and establish the limiting spectra distribution connection between the true BSCA and its noisy observation. Then, based on these theoretical results, we propose an EI-based moments matching method for CSI-related noise level estimation and a rotation invariant estimation method for CSI reconstruction. Based on the cleaned CSI, the quantized precoding problem is tackled via the Bussgang theorem and the Lagrangian multiplier method. The prosed methods are lastly verified by numerical simulations and the results demonstrate the effectiveness of the proposed precoder.