  We have investigated the ($2+1$)-dimensional variable coefficient coupled
nonlinear Schr\"{o}dinger equation (vc-CNLSE) in a graded-index waveguide.
Similarity transformations are used to convert the vc-CNLSE into constant
coefficient CNLSE. Under certain functional constraints we could extract
semirational, multi-parametric solution of the associated Manakov system. This
family of solutions include known Peregrine soliton, mixture of either bright
soliton and rogue wave or dark soliton and rogue wave or breather and rogue
wave. Under a distinct set of self-phase modulation (SPM) and cross-phase
modulation (XPM) coefficients we could establish symbiotic existence of
different soliton pairs as solutions. These soliton pairs may constitute of one
bright and a dark soliton, two bright solitons or two dark solitons. Finally,
when two wave components are directly proportional, we find bright and dark
similaritons, self-similar breathers and rogue waves as different solutions.
