We study the existence and stability of standing matter waves in two quasi onedimensional parallel coupled Bose-Einstein condensates in the presence of a magnetic trap. The system is modeled by linearly coupled Gross-Pitaevskii equations. In particular, the coupled dark soliton solutions are considered. The effect of changing strength of the magnetic trap on the stability of dark solitons is studied. It is found that the presence of a magnetic trap does not affect the stability of coupled dark solitons.