Alpine Linux:FAQ

How do I set the local timezone?

/etc/timezone and the whole zoneinfo directory tree are not supported.
To set the timezone, set the TZ environment variable as specified in
http://www.opengroup.org/onlinepubs/007904975/basedefs/xbd_chap08.html
or you may also create an /etc/TZ file of a single line, ending with a
newline, containing the TZ setting.  For example
echo CST6CDT > /etc/TZ

Source: http://www.uclibc.org/downloads/Glibc_vs_uClibc_Differences.txt

For more information, see how other uClibc-based distributions do this:

• http://leaf.sourceforge.net/doc/buci-tz3.html
• http://www.sonoracomm.com/index.php?option=com_content&task=view&id=107&Itemid=32

For a more complete list of timezones, please see: http://en.wikipedia.org/wiki/List_of_tz_database_time_zones