The baryon-baryon continuum invariant mass spectrum generated from relativistic nucleus + nucleus collision data may reveal the existence of doubly-strange dibaryons not stable against strong decay if they lie within a few MeV of threshold. Furthermore, since the dominant component of these states is a superposition of two color-octet clusters which can be produced intermediately in a color-deconfined quark-gluon plasma (QGP), an enhanced production of dibaryon resonances could be a signal of QGP formation. A total of eight, doubly-strange dibaryon states are considered for experimental search using the STAR detector (Solenoidal Tracker at RHIC) at the new Relativistic Heavy Ion Collider (RHIC). These states may decay to ΛΛ and/or pΞ − , depending on the resonance energy. STAR's large acceptance, precision tracking and vertex reconstruction capabilities, and large data volume capacity, make it an ideal instrument to use for such a search. Detector performance and analysis sensitivity are studied as a function of resonance production rate and width for one particular dibaryon which can directly strong decay to pΞ − , but not ΛΛ. Results indicate that such resonances may be discovered using STAR if the resonance production rates are comparable to coalescence model predictions for dibaryon bound states.