To grow a prefect Money Tree, you will first need to find the seed. A lot of the time you can find one lying around in the town. You will not know what you have at first because it will show in your inventory as a “special seed” of unknown origin. If you can’t find one lying around, you can sometimes catch one when fishing. I do not know if fishing skill affects this or not. Finally, you can sometimes be given the seed as an opportunity in the criminal career.
Unlike most other plants, the Money Tree will not produce something you can re-plant to grow a better quality tree, like a watermelon or garlic plant would for instance. On the upside, they don’t seem to die off like other plants, so long as you fertilize and water them regularly. If you continue to look after and harvest from your Money Tree, it should eventually drop another seed. You can then replant this.
I am not sure if waiting long enough and re-planting the seeds will give you a perfect quality one eventually, because I managed to get the “perfect” status another way. I kept fertilizing my original Money Tree with perfect quality produce (such as fish I had caught) and it raised it’s quality to perfect. Then, when it dropped a seed, I replanted that one. Although my second tree was not a perfect quality one, because my original tree had gained that status, when the second tree was mature, the challenge unlocked.