How to replace an odd-size (2 1/4" x 1 7/8") downspout elbow?
The good news is that your down spout is a simple, plain rectangle tube -- no fancy profile rolled into it as is common with most down spouts.

That's good news because it means you can easily have a new part made. If you want to bang it out yourself you can find rolls of pre-painted "aluminum trim coil" in a range of colors at home centers. First find a large sheet of paper or thin cardboard such as a breakfast cereal box. Work out how to make a series of cuts and folds to form the part you need. You'll have to find edges you can bend the sheet around. The jaw of a vise, the corner or edge of a table, a cut piece of wood -- be creative as you search for objects to help with the forming. You may be able to form the aluminum with your hands, but will probably need to strike it with a hard rubber or urethane hammer to get the bends sharp enough.

Or, if you don't want to earn the Down Spout Making merit badge, find a local contractor who does siding, trim, fascia, gutters, etc. They'll have material in stock as well as tools and machinery for forming custom parts like this. They do it all the time. You could bring them the broken elbow, and maybe a section of the down spout, so that they can custom-make a replacement that fits just right.