PNG is not a lossy image format, so you would likely need to convert the image into another format-- most likely JPEG. JPEG has a settable "quality" factor-- you could simply keep reducing the quality factor until you got an image that was small enough. All of this can be done without changing the image resolution.
Obviously, depending on the image, the loss of visual quality may be substantial. JPEG does best for "true life" images, such as pictures from cameras. It does not do as well for logos, screen shots, or other images with "sharp" transitions from light to dark. (PNG, on the other hand, has the opposite behavior-- it's best for logos, etc.)
However, at 800x600, it likely will be very easy to get a JPEG down under 1MB. (I would be very surprised to see a 30MB file at those smallish dimensions.) In fact, even uncompressed, the image would only be around 1.4MB:
800 pixels * 600 pixels * 3 Bytes / color = 1,440,000 Bytes = 1.4MB
Therefore, you only need a 1.4:1 compression ratio to get the image down to 1MB. Depending on the type of image, the PNG compression may very well provide that level of compression. If not, JPEG almost certainly could-- JPEG compression ratios on the order of 10:1 are not uncommon. Again, the quality / size of the output will depend on the type of image.
Finally, while I have not used ImageMagick in a little while, I'm almost certain there are options to re-compress an image using a specific quality factor. Read through the docs, and start experimenting!
EDIT: Looks like it should, indeed, be pretty easy with ImageMagick. From the docs:
$magick> convert input.png -quality 75 output.jpg
Just keep playing with the quality value until you get a suitable output.
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…