Highly specific molecular imaging with photoacoustics (PA) must suppress background endogenous signals while maintaining signals from target nanoagents. Magneto-motive PA was introduced to perform motion-based background suppression using a low frequency magnetic field. Previous studies show suppression based on displacement magnitude can suffer if significant physiological motion is present. This limitation can be overcome using cyclic magneto-motive PA (cmmPA), where multiple cycles of an ac magnetic field are used and the coherence of detected displacements is the retrieved information. In this paper, we show a method to enhance the magnetic response of an electromagnet specifically for cmmPA. Several magnetic frequencies were tested and a simple model is proposed to describe displacement frequency dependence. By choosing optimal parameters based on this model, we show that the technique can detect a low number of tagged cells using either US-based or PA-based displacement estimation. In addition, robustness to physiological motion is demonstrated in a moving phantom.