Whenever I needed letters like that when I was a kid traveling with on parent, we simply wrote something to the degree of:
To whom it may concern,
My daughter is traveling with her mother named..., they will be traveling for two months in etc etc, She has my permission to travel...etc etc..
Signed and dated.
We just typed it on the computer, printed it out and signed and dated it. Don't know you'll need something more official but this is what we used and we never had any problems.