  We explore two-particle transfer reactions as a unique probe of the occurence
of shape coexistence in shape phase transitions. The (t,p) reactions to the
ground state and to excited $0^+$ states are calculated for the isotope chain
of even-even Zirconium isotopes starting from stable nuclei up to beyond
current experimental limits. Two-particle spectroscopic factors derived from
Monte Carlo Shell Model calculations are used, together with the sequential
description of the two-particle transfer reaction mechanism. The calculation
shows a clear signature for a shape phase transition between $^{98}$Zr and
$^{100}$Zr, which displays coexistence of a deformed ground state with an
excited spherical $0^+$ state. Furthermore, we show that there is a qualitative
difference with respect to the case of a normal shape phase transition that can
be discriminated with two-neutron transfer reactions.
