  We present an efficient and robust source of photons at the $^{87}$Rb D1-line
(795 nm) with a narrow bandwidth of $\delta=226(1)$ MHz. The source is based on
non-degenerate, cavity-enhanced spontaneous parametric down-conversion in a
monolithic optical parametric oscillator far below threshold. The setup allows
for efficient coupling to single mode fibers. A heralding efficiency of
$\eta_{\mathrm{heralded}}=45(5)$ % is achieved, and the uncorrected number of
detected photon pairs is $3.8 \times 10^{3}/(\textrm{s mW})$. For pair
generation rates up to $5\times 10^{5}/$s, the source emits heralded single
photons with a normalized, heralded, second-order correlation function
$g^{(2)}_{c}<0.01$. The source is intrinsically stable due to the monolithic
configuration. Frequency drifts are on the order of $\delta/20$ per hour
without active feedback on the emission frequency. We achieved fine-tuning of
the source frequency within a range of $ > 2$ GHz by applying mechanical
strain.
