How to change the frame color in Keynote
As far as I can see, the answer would have to be no.

The options for changing the colours of picture frames are greyed out, and in all the many keynotes I have seen, green frames have never been included.

That is not to say it is impossible.

It may be possible to make one, like this.

Create a rectangle of a shade of colour 50% brighter than the desired shade.
Create two identically sized photos the first with a frame.
Set the framed photo to 50% opacity, and position it over the rectangle.
Finally, place the good photo over the frame, and hope it was worth the effort.

I hope this helps, somehow.