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We construct various systems of coherent states (SCS) on the$O(D)$-equivariant fuzzy spheres $S^d_\Lambda$ ($d=1,2$, $D=d\!+\!1$)constructed in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451] andstudy their localizations in configuration space as well as angular momentumspace. These localizations are best expressed through the $O(D)$-invariantsquare space and angular momentum uncertainties$(\Delta\boldsymbol{x})^2,(\Delta\boldsymbol{L})^2$ in the ambient Euclideanspace $\mathbb{R}^D$. We also determine general bounds (e.g. uncertaintyrelations from commutation relations) for$(\Delta\boldsymbol{x})^2,(\Delta\boldsymbol{L})^2$, and partly investigatewhich SCS may saturate these bounds. In particular, we determine$O(D)$-equivariant systems of optimally localized coherent states, which arethe closest quantum states to the classical states (i.e. points) of $S^d$. Wecompare the results with their analogs on commutative $S^d$. We also show thaton $S^2_\Lambda$ our optimally localized states are better localized than thoseon the Madore-Hoppe fuzzy sphere with the same cutoff $\Lambda$.

On localized and coherent states on some new fuzzy spheres