i-adjective
Dated term; modern Japanese normally uses 好ましい (このましい) instead. Still understood, but sounds old-fashioned.
See also: 好ましい
In old novels, you see expressions like 'a likeable young man'.
今では「好もしい」より「好ましい」のほうが普通だ。
Nowadays, 好ましい is more common than 好もしい.