Both Don't be discouraged and Don't be disappointed are perfectly natural things to say, and in many contexts they'll effectively mean the same thing - speaker is advising someone to look on the bright side (to find good things in a bad situation).
As OP has discovered, the dictionary definitions are somewhat different, but they're obviously closely related. A "defeatist" reaction to finding yourself in a bad situation might include either or both of disappointment and discouragement, but in practice using either word will often imply the other anyway.
But if we include an "intensifier" like ever / never, there's a good reason why Don't ever be disappointed is far less likely advice than Don't ever be discouraged.
When you're already in some specific "bad situation" to which you're reacting negatively (disappointment and/or discouragement), people may quite naturally advise you to change your reaction (often, you can't change the situation itself, just your reaction to it).
But when ever / never is included in the utterance, it's non-specific "lifetime advice". And the obvious way to avoid ever being discouraged is to have more courage / faith / optimism (as a positive permanent aspect of your character, not just a reaction to a specific situation).
On the other hand, the most obvious way to avoid ever being disappointed (through some permanent aspect of your character) is to be a life-long pessimist (never get your hopes up in the first place). But being a pessimist is generally thought of as a negative character attribute, so people won't often advise you to go down that path.
In any specific situation, you might avoid disappointment by putting in a lot of effort to ensure nothing goes wrong. But as "lifetime advice" that approach won't mean you'll never be disappointed, because lots of bad situations are unforeseeable and/or unpreventable. Clearly it makes a difference whether someone's advising you to change your reaction to a specific situation, or to avoid ever having that reaction.
In short, permanently avoiding discouragement implies being courageous / resolute (good attribute), whereas permanently avoiding disappointment implies lacking hope / ambition (bad attribute).
Note that idiomatic You're hopeless! doesn't mean You lack optimism - it means You're useless!