I muddled my way through using scalebox
, although I don't know how to get it to change the relative size rather than absolute:
$\lim\limits_{\scalebox{0.4}{$\Delta P \to 0$}}$
or this, which looks slightly better:
$\lim\limits_{\scalebox{0.6}{$^{\Delta P \to 0}$}}$
or even better:
$\lim\limits_{\scalebox{0.7}{$\scriptstyle\Delta P \to 0$}}$