  We report a search for narrow resonances, produced in $p\bar{p}$ collisions
at $\sqrt{s}=1.96$ TeV, that decay into muon pairs with invariant mass between
6.3 and 9.0 GeV/c^2. The data, collected with the CDF~II detector at the
Fermilab Tevatron collider, correspond to an integrated luminosity of 630
pb$^{-1}$. We use the dimuon invariant mass distribution to set 90% upper
credible limits of about 1% to the ratio of the production cross section times
muonic branching fraction of possible narrow resonances to that of the
$\Upsilon(1{\rm S})$ meson.
