According to the dictionary on my MacBook Pro, ありあまる means "be [have*] more than enough". I was thinking about the song by ゲスの極み乙女:ロマンスがありあまる when I first heard the word/expression.
The question boils down to if I can use ありあまる as a positive expression
ロマンスがありあまる I have lots of romance, and that is a good thing
or a negative expression
ロマンスがありあまる I am fed of with romance, and that is a bad thing
Or maybe it is context dependent?
The dictionary also provides me with two examples
▸ 精力が有り余っている have too much [an excess of] energy.
▸ 彼には有り余るほどの金がある He has more money than he can spend.
But I still do not know if they are meant as negative or positive.