The ``problem of time'' has been a pressing issue in quantum gravity for some
time. To help understand this problem, Rovelli proposed a model of a two
harmonic oscillators system where one of the oscillators can be thought of as a
``clock'' for the other oscillator thus giving a natural time reference frame
for the system. Recently, the author has constructed an explicit form for the
coherent states on the reduced phase space of this system in terms of Klauder's
projection operator approach. In this paper, by using coherent state
representations and other tools from coherent state quantization, I investigate
the construction of gauge invariant operators on this reduced phase space, and
the ability to use a quantum oscillator as a ``clock.''Comment: 13 pages, Late
