You should use **`-e`** with `echo` as follows:
echo -e ${string/abab/'\
'}
From manpage:
-e enable interpretation of backslash escapes
If -e is in effect, the following sequences are recognized:
\\ backslash
\a alert (BEL)
\b backspace
\c produce no further output
\e escape
\f form feed
\
new line
\r carriage return
\t horizontal tab
\v vertical tab