In the last twenty years, both free fall and interferometry/deflectometry experiments have been proposed for the measurement of the gravitational acceleration on positronium, which is a purely leptonic matter-antimatter atom formed by an electron and its antiparticle (positron). Among the several challenges posed by these experiments is the development of position-sensitive detectors to measure the deflection of positronium in the Earth's gravitational field. In this work, we describe our recent progress in the development of position-sensitive detectors. Two different detection schemes are considered. The first is based on Ps ionization in a strong homogeneous magnetic field and imaging of the freed positron with a microchannel plate. The second scheme is based on scanning the positronium atom distribution on a plane by moving the slit or a material grating with sub-nm accuracy, and counting the atoms crossing the obstacle and those annihilating on it. The possibility of reaching a spatial resolution of around 15 μm using the former detection scheme is shown, and preliminary steps towards the development of a detector following the latter scheme (with potential position sensitivity in the sub-nm range) are described.