The intensification of cropping systems in the salt-affected coastal zones of the Ganges Delta can boost food security in the region. The scarcity of fresh water, coupled with varying degrees of soil and water salinity are however limiting factors for the expansion of irrigated cropping in that area. In this study, we assessed the potential of growing sunflowers using combinations of low and medium saline water for irrigation. The experiments were conducted at two locations with six irrigation treatments in 2016–2017 and 2017–2018. The treatments were: T1—two irrigations at early vegetative (25–30 days after sowing; DAS) and flowering stages (60–65 DAS) with low salinity water (LSW, electric conductivity, ECw < 2 dS m−1); T2—two irrigations, one at the vegetative stage with LSW and one at the flowering stage with medium salinity water (MSW, 2 < ECw < 5dS m−1); T3—two irrigations, one at the vegetative stage with LSW and one at seed development stage (75–80 DAS) with MSW; T4—three irrigations at the vegetative, flowering and seed development stages with LSW; T5—three irrigations, at vegetative stage with LSW, and flowering and seed development stages with MSW; and T6—three irrigations, two at the vegetative and flowering stages with LSW and one at the seed development stage with MSW. Irrigation with LSW at early growth stages and MSW at later growth stages did not significantly (p < 0.05) affect the yield compared to the LSW irrigation at early and later growth stages. Crop water productivity and irrigation water productivity of sunflowers (p < 0.001) increased substantially with the decreasing amount of irrigation water with an average of 1.18 kg m−3 and 2.22 kg m−3 in 2017 and 0.92 kg m−3 and 1.29 kg m−3 in 2018, respectively. Grain yield was significantly correlated with root zone solute potential. The flowering and seed development stages of sunflowers in February–March were sensitive to both low and medium saline water irrigation for seed yield. Overall, the results show that irrigation with LSW (ECw < 2dS m−1) at early growth stages and MSW (2 < ECw < 5dS m−1) at later growth stages could be an option for dry-season sunflowers in the coastal zones of the Ganges Delta which would allow double cropping in this area.