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There is no timelike Killing vector for FRW cosmologies. In the path integral formalism, is it possible to Wick rotate for quantum cosmology in quantum gravity? If yes, how? If no, how does one work with nonconvergent Lorentzian path integrals?

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Hartle and Hawking treated deSitter space, for which there isn't a global timelike Killing vector, but they worked in the patch for which static deSitter coordinates are applicable - here the "t" Killing vector is timelike, and they could perform the Wick rotation. –  twistor59 Nov 30 '12 at 8:48
You might be interested in the e-print "Canonical Quantization of a Closed Euclidean Universe with a Cosmological Constant" arXiv:gr-qc/9909002 –  Alex Nelson Nov 30 '12 at 16:45

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