This is what I did. I knew the backing wasn't far off one of the colours of the animals in the print on the top. I opted to take two strips of it for part of the binding, but the binding was going on the quilt in a particular way.

I measured the entire length of the quilt and it came out to be 29 1/2". The middle would be 14 3/4" and that is where I placed a pin. I did that on both sides and then laid my yard stick across to make sure both pins lined up.

I auditioned the grey piece of binding all the way around the bottom edge of the quilt to make sure the join would not be on a corner. It fell right there, so I moved the starting point.
To start both the grey and the yellow binding I measured down 4" from the centre of the LONG side and started sewing from there. I stopped both 4" from the ending. I had to make a join of the two fabrics on the sides and I needed fabric lengths to do it.

I sew the whole section of one colour. Stop. Then sew the entire section of the second colour.
I do a straight join instead of an angle join. It is just a preference thing. 
When I trim away the excess I leave a 3/8" seam allowance versus a 1/4". Another preference when I work with flannelette. It does take a bit of time to do this type of binding instead of one with all the same fabric, but when you run out, sometimes you have to just make do. Time for some hand sewing!!