In this paper, we consider variable-rate variable-power MQAM modulation employed under delay quality-of-service (QoS) constraints over spectrum-sharing channels. In particular, we assume two users sharing the spectrum with one of them having a primary access to the band, and the other, known as secondary user, constrained by interference limitations imposed by the former. We study the performance of the secondary user's link employing adaptive MQAM modulation scheme when, on top of the above-mentioned interference constraint, the secondary user is also required to satisfy a statistical delay QoS constraint. Considering two modulation schemes, namely, continuous MQAM and discrete MQAM with restricted constellations, we obtain the effective capacity of the secondary user's link, and derive the optimum power allocation scheme that maximizes the effective capacity in each case. Numerical simulations are conducted to corroborate our theoretical results.