I think this may be a misunderstanding: even though gern is often translated as a verb ('like'), it isn't a verb - it is an adverb (similar to 'gladly', 'happily'). A more literal translation would be 'I play football gladly' (of course it wouldn't sound idiomatic in English). The only verb in this sentence is spiele. So, the sentence follows the usual German word order: the verb is in second position: Ich spiele Fußball gern = Ich spiele gern Fußball.
I think, stylistically, the position of the adverb gern sounds really bad in your version: Usually you would not include more than one phrase in the post-field of a sentence. Fussball spielen (the activity) forms a sentence bracket here, so it should be:
Ich spiele gern Fussball, wenn es sonnig ist.
Maybe, it would be a little better if you mark the multiple occupation of the post-field with an extra comma (or short pause when saying the sentence)
Ich spiele Fussball, gern, wenn es sonnig ist.
..., but that would mean sth. else like:
(Yes,) I (do) play soccer, (I like it) all the more when it's sunny.