1. Open the app icon in Photoshop.
2. From the File menu, select Save for Web.
3. At the top right, you'll see a drop-down with "PNG-24." Change that to "PNG-8."
4. A new drop-down for "Colors" will appear to the right. This will usually default to 256. Decrease the colors until your file size (visible at the bottom left of the window) drops down to 500 KB or lower.
5. Save your file, and upload it in Publish!