Song is the right one for crazy American girl to cover (8)
I believe the answer is:
madrigal
'song' is the definition.
(madrigal is a kind of song)
'the right one for crazy american girl to cover' is the wordplay.
'the right one for' becomes 'ri' (I can't justify this - if you can you should give a lot more credence to this answer).
'crazy' becomes 'mad' (synonyms).
'american girl' becomes 'gal' (US term for a girl).
'to cover' indicates putting letters inside.
'mad'+'gal'='madgal'
'ri' placed inside 'madgal' is 'MADRIGAL'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for madrigal that I've seen before include "Without exaggeration" , "Elaborate part song" , "air" , "Old part song" , "Unaccompanied harmonised part song" .)