If you already have a good idea what the force-deflection relationship due to the permanent magnets is, you might try defining a nonlinear spring (or combination of nonlinear springs if needed) to mimic the magnetic forces. The spring in the image below connects a pair of remote points (one of which is "free standing"):
You can then apply remote displacement(s) to the remote point(s) to "preload" the spring(s) if you want to define non-zero forces acting at zero beam deflection.
If, on the other hand, you want to use FEA to calculate the magnetic field and associated forces, you could use coupled field elements. The coupled field element options that include magnetic DOFs are not natively exposed in Mechanical, but they can be defined with command objects. If motion is large enough to excessively distort the "air" mesh in the gap between the beam tip and the fixed PMs, you might replace the elements types created by Mechanical with legacy SOLID5/98, which use the magnetic scalar potential for magnetostatic field calculations (induced eddy curents are not accounted for). In a "large motion" application, these have a companion contact element (CONTA174 with keyopt(1)=7) that you might use in a "sliding interface" in the "air" to relieve mesh distortion.
Yet another option for calculating magnetic forces might be to use system coupling between Maxwell and Mechanical.