The best replacement for parse is stackmob.

The best alternatives to parse are rated as following:
★★★★★  stackmob
★★★★★  firebase
★★★★  aws
★★★★  tryparse
★★★  urban airship
★★★  convert
★★★  kinvey
★★  azure
★★  heroku
★★  convert c#
★★  appcelerator
★★  google app engine
★  google cloud
★  apigee
★  phonegap
★  pass
★  convert c
★  appengine
★  parseexact
★  convert toint32
★  convert.todatetime
★  eval
  convert.toint32
  datetime parseexact

Your alternative for parse is not listed? Suggest!
Speaking about parse, one probably shouldn't forget about core data.

Other search terms related to parse and their ratings are:
★★★★★ core data
★★ phonegap
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Google Trends

Scale is based on the average worldwide traffic of parse in all years. Click on graph for more.
parse
stackmob
firebase