Lets try...
(1) decision: map ə, ɔ, ŋ, to (ALTGR+ e c n )
(2) using xmodmap command get the current definition of those chars (e,c,n):
xmodmap -pke | grep '= [ecn] ' > myfon.xmap
myfon.xmap has 3 lines like:
keycode 26 = e E e E EuroSign cent e E e E
keycode 54 = c C c C cent copyright cent copyright c C
keycode 57 = n N n N n N n N n N
(3) ALTGR is the 5th column; replace it by the unicode of 'ə, ɔ, ŋ,' ( ipa-unicode )
keycode 26 = e E e E U0259 cent e E e E
keycode 54 = c C c C U0254 copyright cent copyright c C
keycode 57 = n N n N U014b N n N n N
(3) activate this keyboard redefinition: `xmodmap myfon.xmap`
(4) press (altgr+e) and pray...