Clark,

A simple, maybe crude, way is to cut it at the side Anchor Points with the Scissors Tool and change the colour of the bottom half.

You can do this with Gradients on Strokes.

Set the stroke to have a white to black gradient (the default gradient)

Click the white gradient stop and enter 50 in the Location field. Click the black gradient stop and enter 50 in the location field.

Change the angle field to whatever you want. 90° in my image so top is black bottom is white.

Grey circle added behind so the white can be seen here.

The interior of my circle is transparent. The grey you see is simply another circle behind it so the white shows up.

Clark, others,

I really like the way Scott suggests.

However, I believe, as always, that there are always different ways of doing things, each in its own right. Each way may serve some purposes better than others (in both senses).

If we look at simplicity/efficiency, and just compare the (count of) steps that differ between the suggestions in posts #1 and 7.

For a first use, #1 requires 2 cllicks with the Scissors Tool and 1 setting of each colour to change, whereas #7 requires 3 settings of gradient stop positions and 2 settings of  colour (4 for other colours than black and white).

For a subsequent use, #1 requires 1 setting of each colour to change, whereas #7 requires 2 settings of gradient stop positions and 2 settings of each colour to change.

It should be noted that neither #1 nor #7 imply any fill.

It seems that everything said here confirms the equality of different solutions.

And grouping is easy, making paths operable together.

I also like the solutions presented by Steve and Emil. And the one by Larry was quite obvious for the other possible interpretation of the OP.

If I had to choose a favourite in this case, it might be the one by Emil, as I understand it (rather than how I read it), namely to create the circle, copy it to the front, delete the top (or bottom) Anchor Point, and change the colour of the still selected halved circle, then group.