Dual-functional radar-communication (DFRC) is a promising technology where radar and communication functions operate on the same spectrum and hardware. In this paper, we propose an algorithm for designing constant modulus waveforms for DFRC systems. Particularly, we jointly optimize the correlation properties and the spatial beam pattern. For communication, we employ constructive interference-based block-level precoding (CI-BLP) to exploit distortion due to multi-user and radar transmission. We propose a majorization-minimization (MM)-based solution to the formulated problem. To accelerate convergence, we propose an improved majorizing function that leverages a novel diagonal matrix structure. We then evaluate the performance of the proposed algorithm through rigorous simulations. Simulation results demonstrate the effectiveness of the proposed approach and the proposed majorizer.