We present measurements of tunneling magnetoresistance (TMR) in single-wall carbon nanotubes attached to ferromagnetic contacts in the Coulomb blockade regime. Strong variations of the TMR with gate voltage over a range of four conductance resonances, including a peculiar double-dip signature, are observed. The data are compared to calculations in the “dressed second order” (DSO) framework. In this nonperturbative theory, conductance peak positions and linewidths are affected by charge fluctuations incorporating the properties of the carbon nanotube quantum dot and the ferromagnetic leads. The theory is able to qualitatively reproduce the experimental data.