Perfect absorption (PA) of incident light is important for both fundamental light-matter interaction studies and practical device applications. PA studies so far have mainly used resonant nanostructures that require delicate structural patterning. Here, we realize tunable and broadband PA in the near-infrared region using relatively simple thin film coatings. We adjust the growth condition of an ITO film and control its epsilon-near-zero (ENZ) wavelength. We show that this results in highly tunable PA in the telecommunication window. Then, using an ITO multilayer of different ENZ wavelengths, we demonstrate broadband PA that covers a wide range of near-infrared wavelengths. The use of ENZ coatings makes PA adjustable during the film growth and does not require any structural patterning afterward. It also facilitates the chip-scale integration of perfect absorbers with other device components. Broadband PA relaxes the single wavelength condition in previous PA studies, and thus it is suitable for many practical device applications, including sensors, photodetectors, and energy harvesting devices.