The best replacement for picnik is picasa.

The best alternatives to picnik are rated as following:
★★★★★  picasa
★★★★  photoshop
★★★★  fotoflexer
★★★  aviary
★★★  phixr
★★★  snipshot
★★★  gimp
★★★  drpic
★★★  splashup
★★★  pixenate
★★★  adobe photoshop express
★★  pixlr
  piknik
  picmonkey
  photoscape
  photoshop express

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

Other search terms related to picnik and their ratings are:
★★★★★ picasa
★★★★★ google plus
You have in mind a companion for picnik and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of picnik in all years. Click on graph for more.
picnik
picasa
photoshop