Notifications are greyscale as explained below. They are not black-and-white, despite what others have written. You have probably seen icons with multiple shades, like network strength bars.
Prior to API 21 (Lollipop 5.0), colour icons work. You could force your application to target API 20, but that limits the features available to your application, so it is not recommended. You could test the running API level and set either a colour icon or a greyscale icon appropriately, but this is likely not worthwhile. In most cases, it is best to go with a greyscale icon.
Images have four channels, RGBA (red / green / blue / alpha). For notification icons, Android ignores the R, G, and B channels. The only channel that counts is Alpha, also known as opacity. Design your icon with an editor that gives you control over the Alpha value of your drawing colours.
How Alpha values generate a greyscale image:
Changing it up with setColor:
Call NotificationCompat.Builder.setColor(int argb). From the documentation for Notification.color:
Accent color (an ARGB integer like the constants in Color) to be applied by the standard Style templates when presenting this notification. The current template design constructs a colorful header image by overlaying the icon image (stenciled in white) atop a field of this color. Alpha components are ignored.
My testing with setColor shows that Alpha components are not ignored. Higher Alpha values turn a pixel white. Lower Alpha values turn a pixel to the background colour (black on my device) in the notification area, or to the specified colour in the pull-down notification.