The simple solution is buy two plates of each color.
There may be times when your children will not be able to have what they desire. (Maybe. Philosophies differ on that.)
This is not one of those times.
You should decide what lesson you want to convey.
Some people want to convey the lesson, "Even the simple things in life are hard to get or achieve." I don't like that lesson, don't agree with it, and don't wish to convey it to my son.
Another philosophy is that one can always get what one wants or dreams of, given sufficient intention to achieve it and sufficient hard work and planning.
I like this lesson, more or less, and would be happy to convey it to my son. This would suggest an approach of making the child responsible for earning the money to buy the additional desired plate. But for something as simple as an extra plate, I might just buy it. (Also see notes below concerning EXCHANGE.)
Perhaps you wish your son to be polite. That I can agree with.
However, politeness is not the senior attribute for all of life. I want to make some outrageous analogies that are less in response to you (the Original Poster) and more in response to various comments and other attitudes on this subject I've observed in life:
You have to consider what your own intentions really are if you don't want to purchase another plate. And determine if you are truly working toward a desirable goal, or just aren't willing for the kid to get what he wants (a "can't have" attitude).
To give an outrageous reductio ad absurdum example, probably offensive, imagine someone striking a screaming child repeatedly and saying, "I'm going to teach him some manners! I'm not going to stop until he asks me politely." What motivates this? Maybe a lot of things, but certainly not a clear-cut wholesome desire for the child's improvement.
One of the things that might motivate it would be a convoluted ideology that "Life is awful tough and if you don't learn to take your lumps without screaming now, you'll have to learn it later when the lumps won't be administered by a loving parent like me."
None of this is related to actually improving the child, despite the justifications used. (If you disagree, perhaps time for some introspection.)
I make that wild analogy because it's the same mental mechanism behind denying the child what he wants simply because it may not always be possible to fulfill the desire.
The most important factor is exchange. Exchange is something in return for something. This exchange does not have to be with money.
When the child is very young the exchange may be simply asking nicely, or it may be making you smile and laugh. That is his (or her) contribution. You can reward that with an extra plate. (I'm not saying you will explicitly label it as a reward.)
When the child is older and wants a new bicycle, you may work out other exchange. When he or she wants a car, the teenager may have to produce and contribute and exchange with other people to earn the money necessary to buy a car.
The type of exchange will change; the fact of exchange will not.
You should avoid the child reaching the point where he believes he can get anything he wants with no exchange or contribution on his part whatsoever. But you should also avoid engendering the belief that he can't get what he wants no matter what he does or contributes.
The contention on this answer (six upvotes and three downvotes at this writing) is interesting.
I'm addressing this specific question, not some hypothetical other question which may or may not be similar. In fact, my basic premise here is that:
The key to handling this situation is to not equate it with other situations.
Your kids both want a green plate. Fine, get two green plates. Handled.
Yes, there are other things they really can't both have, but plates is not one of them.
When you encounter other things they really can't both have, get them to understand the real reasons why not.
And they'll know you're telling the truth, because they'll know by experience (green plates) that if there weren't any real reasons for them not to have it, they could have it.
If you can't explain the reason to the kid in a persuasive way that they can understand and agree with, there's probably something wrong with your reason.
Try getting a kid to understand: "No, you can't have a plate, because then when there are other things that you can't have, you won't understand why you can't have them." Factually, that reason makes absolutely no sense at all.