Submarine canyons along the coast play a major role in upwelling dynamics. On the one hand, various numerical studies and observations have suggested a depth origin of upwelling in submarine canyons between 100 and 400 m deep. On the other hand, recent observations in the Cassidaigne canyon, Northwest of the Mediterranean Sea, show wind-driven transient upwelling of water at depths of over 1600 m. The potential impact of interior stratification on upwelling depths in submarine canyons is investigated using CROCO numerical simulations. A 6-day alongshore upwelling-favorable wind is considered. The dataset gathers the results of three idealized simulations: - A coastal shelf slope without any canyon under non-stratified condition; - A coastal  slope with a canyon under non-stratified condition (analog to the particular case of the Mediterranean Sea); - A coastal slope with a canyon under stratified condition (comparable to the stratification in most oceanic areas). The results highlight a control of the upwelling flow and depth with the stratification. A non-stratified water column leads to upwelling over the entire water column, from the deep sea to the mixed layer depth. A stronger stratification results in a tilting of the isopycnals at the canyon head as a response of free surface elevation. This adjusment eliminates pressure gradients in the canyon body, essential for generating upwellings in canyons, and then limits deep currents. The numerical code configuration (CROCO) is provided.