If there is a stone-size moonlet orbiting around Mars, can we detect it?
Depends on what you mean by a small stone and if it has to be in a long-term stable orbit around Mars. According to Mark Adler et al. in the Use Of MRO Optical Navigation Camera To Prepare For Mars Sample Return, JPL 2012 (PDF), the Mars Reconnaissance Orbiter's Optical Navigation Camera (ONC) could be used to detect small Mars' satellites:
Unknown small satellites may exist in the inner region of the Martian system. The current-best searches (Viking, Hubble) have claimed limits of roughly 50 to 100 meters with no detections. In the region out to Phobos' orbit, the ONC could detect objects as small as one to a few meters diameter during normal spacecraft nadir-pointed operations (that is, with no special pointing or spacecraft attitude maneuvering), and to roughly tens of meters out to Deimos.
Possible use of ONC to detect postulated dust rings through forward-scattered light is also mentioned. So it depends on their size, orbital altitude and albedo.
There is however no good reason to believe that really tiny, pebble or a small stone-sized moonlets would be long-term stable in orbit around Mars. Mars is still relatively close to the Sun with its semi-major axis at about 1.52 AU (Earth's is 1 AU), unlike the Earth has only weak remnant crustal magnetism, and small orbiting objects would carry small momentum, so they could be relatively easily perturbed by various mechanisms of the Sun's activity (direct interaction with coronal mass ejections, radiation pressure in combination with Yarkovsky effect, YORP effect, Lidov–Kozai mechanism, Poynting–Robertson effect), lose momentum or exchange inclination for eccentricity, and eventually precess out of orbit.
It is possible that shorter-term Mars moonlets exist, or are in stable resonance with Phobos and Deimos, but that's, in my opinion, a long shot. So, in short, we could detect moonlets in the size/mass range that would carry enough momentum to be in long-term stable orbit around Mars, if we systematically searched for them. And smaller than perhaps boulder-sized moonlets most likely don't exist. Last event that had the potential for capture of such small moonlets was C/2013 A1 Siding Spring Mars flyby on 19 October 2014. Its own trajectory and speed would be prohibiting for any gravitational capture of small debris into orbit around Mars, but secondary debris, such as products of collisions with Phobos or Deimos aren't excluded for certain.