Large notification icon background

You could use icon with transparent background as large icon for notification. Also you could tint large and small icons.
As already said use setColor() to tint small icon.
And for the large icon use this function:

fun Bitmap.tint(color: Int): Bitmap =
    Bitmap.createBitmap(this.width, this.height, Bitmap.Config.ARGB_8888).also { outBmp ->
        Canvas(outBmp).drawBitmap(
            this, 0f, 0f,
            Paint().apply {
                this.colorFilter = PorterDuffColorFilter(color, PorterDuff.Mode.SRC_IN)
            }
        )
    }

So your code will look like this:

    NotificationCompat.Builder(context)
        .setColor(yourColor)
        .setLargeIcon(largeBitmap.tint(yourColor))
        .setSmallIcon(R.drawable.small_icon)

Here what you could get on Android 5.0: On Android 10:

Yes, the color of the large icon is part of the actual image. The dimensions of the large icon on lollipop are 40x40dp with a optical view filling the entire image. So you should create an asset of 40x40dp with a circle of a 20dp radius. You can set the notification's large icon as follows:

NotificationCompat.Builder mBuilder = new NotificationCompat.Builder(context)
    .setSmallIcon(R.drawable.notification_small_icon)
    .setLargeIcon(notificationLargeIconBitmap)
    .setContentTitle("Notification")
    .setContentText("Content text")
    .setColor(context.getResources().getColor(R.color.accent_color));

If you need the large icon to be from a drawable resource you can get a Bitmap instance like this:

Bitmap notificationLargeIconBitmap = BitmapFactory.decodeResource(
    context.getResources(), 
    R.drawable.notification_large_icon);

If you want your notification to be displayed nicely with previous versions of android (kitkat and below), you should have a squared version of your large icon with a dimension of 64x64dp.