In quasi-1D pi-conjugated polymers such as trans-polyacetylene and polyenes, electron correlation effects determine the "reversed" excited state ordering in which the lowest two-photon 2A(g) state lies below the lowest one-photon 1B(u) state. In this paper, we present conclusive theoretical evidence of reversed excited state ordering in fairly 2D pi-conjugated systems, namely, diamond-shaped graphene quantum dots (DQDs). Our electron correlated calculations show that DQDs begin to exhibit reversed excited ordering with increasing size, in disagreement with independent-particle picture. This signals the onset of strong correlation effects which renders them nonluminescent. Further, we calculate and analyze the two-photon absorption (TPA) spectra as well as photoinduced absorption (PA) spectra of these systems and find excellent agreement with the available experimental results. Our investigations demonstrate that unlike a strictly 1D system like trans-polyacetylene, the nonlinear and excited state absorptions in DQDs are highly intricate, with several even parity states responsible for strong absorptions. Our results could play an important role in the design of graphene-based nonlinear optical devices.