Yes: put "JULIA_CPU_TARGET = core2" in julia/Make.user
This will generate the system image with the instruction set available on core2 (so no AVX, for example). Should be fine on Xeon, but not sure about Operon and CoreDuo.
If this is still an issue, or there is a newer baseline ISA that will work on all of your systems, you should be able to target something other than core2 with a few modifications. See the following commit and discussion for more information:
Regarding performance: if you are not using 'userimg.jl' to precompile user code into the system image, then the target ISA of the system image should have little effect overall because user code will be JIT'd against the actual processor.