Is there a good, natural way to produce naltrexone?

No. Naltrexone is a synthetic pharamceutical. I know of no "natural" way to produce it, but it is readily available (with a prescription) from pharmacies.
No. But why? naltrexone blocks opioid receptors. I would understand your question if you would ask how you can produce opioid agonists naturally, but cannot imagine why you need to block your receptors naturally. Naltrexone is not expensive. For some conditions, very low dose of naltrexone is working better than the high dose. tell me more about your question and I might know the answer.
No. There are no known ways to induce the body to make opioid antagonists - why should there be? Endorphins, our own opioids, are critical to our happiness, our ability to combat pain, to exercise and many other things. Naltrexone is a semi-synthetic opioid than can only be made from the poppy plant and other chemicals in a lab.