$\mathrm{◇}$ is equivalent to $\mathrm{♣}$ and continuum hypothesis

If $S$ is a stationary subset of $\kappa$ and implies $2^{\lambda }\le \kappa$ then

$${\mathrm{◇}}_S\leftrightarrow {\mathrm{♣}}_S$$

Moreover, this is best possible: $\mathrm{\neg }{\mathrm{◇}}_S$ is consistent with ${\mathrm{♣}}_S$.