Two-dimensional (2D) materials have recently been explored as a potential for saturable absorbers (SA) due to their remarkable optoelectronic and nonlinear optical properties. In this work, we have experimentally reported the 2D boron carbon oxynitride (BCNO) as a potential mode-locker in erbium-(EDFL) and thulium-doped fiber lasers (TDFL) for the first time. The BCNO-coated arc-shaped fiber was explored as a novel optical loss modulator and exhibited a modulation depth of 8.2 % and 5 % at 1.5 µm and 2 µm, respectively. The mode-locked laser was then achieved by using BCNO-coated arc-shaped fiber in EDFL having a pulse width, repetition rate, and center wavelength of 1.56 ps, 19.14 MHz, and 1562.2 nm, respectively. Mode-locked pulses of 1.456 ps duration were achieved by incorporating BCNO-coated arc-shaped fiber in TDFL, operated at center wavelength, repetition rate, and signal-to-noise ratio (SNR) of 1944 nm, 13 MHz, and 70.3 dB, respectively. These results prove BCNO to be a promising low-cost 2D material to be further explored for laser-related applications.