The best replacement for coincidence is fate.

The best alternatives to coincidence are rated as following:
★★★★★  fate
★★★  destiny
★★★  irony
★★  conspiracy
★★  coincident
★  synchronicity
★  sign
★  miracle
★  divine intervention
★  providence
★  psychic
★  meant to be
  causation
  god's plan
  causality
  serendipity
  miracles
  ironic
  signs
  cause and effect
  premonition
  correlation
  happenstance

Your alternative for coincidence is not listed? Suggest!
Speaking about coincidence, one probably shouldn't forget about irony.

Other search terms related to coincidence and their ratings are:
★★★★★ irony
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Google Trends

Scale is based on the average worldwide traffic of coincidence in all years. Click on graph for more.
coincidence
fate
destiny