in GIMP, do the following:
>select the select by color tool
>click the transparent area
>go to Select > Feather selection
>Put the number 1 or whatever you feel will be right.
>Confirm (or okay or apply or whatever the forget.)
>Press delete.
>Save.
>Filters>Enhance>Antialias
^i didn't know this existed until now holy stuff.
eh, you're better off just using the blur tool with a really small brush.