Perhaps you can use the MS Word shortcut, CtrlShift^ to add the diacritic to Alt237. You might also try changing the keyboard layout to add dead-key composition of characters.
One issue is that, though there are some Greek characters that traditionally may be written with diacritics, accented φ is not one.There are lists, such as at Keynote Support, that show the key press combinations for standard accented characters, such as the following, (tested in LibreOffice Writer):
- Alt912 for ΐ, iota with dialitika and tonos, or
- Alt942 for ή, eta with tonos.
Another issue is that other diacritics may be composed, but accent circumflex is not.
A third issue is that the two Greek marks for accent circumflex are notthat used in the Latin alphabet: ῟, ἇ, ἧ, and ᾧ, and ῁, ῗ, and ῧ.