The best replacement for zlib is gzip.

The best alternatives to zlib are rated as following:
★★★★★  gzip
★★★  bzip2
★★★  deflate
★★  lzma
★★  libz
★★  snappy
★★  zlibc
★  lz4
★  quicklz
★  lzo
★  mini z
★  libzip
★  zip
  bz2
  gzhandler
  lzop
  mod_deflate

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

Other search terms related to zlib and their ratings are:
★★★★★ gzip
★★★★ openssl
You have in mind a companion for zlib and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of zlib in all years. Click on graph for more.
zlib
gzip
bzip2