  We show that arithmetic lattices in $\mathrm{SL}_{2}(\mathbb{R})$, stemming
from the proper units of an Eichler order in an indefinite quaternion algebra
over $\mathbb{Q}$, admit a `small' covering set. In particular, we give bounds
on the diameter if the quotient space is co-compact. Consequently, we show that
these lattices admit small generators. Our techniques also apply to definite
quaternion algebras where we show Ramanujan-strength bounds on the diameter of
certain Ramanujan graphs without the use of the Ramanujan bound.
