I understand 'cheer' here in the sense given in the OED at 5.b
That which brings joy, gladness, or comfort; solace; encouragement
Specifically relevant would be the idea of 'comfort' and 'solace'.
Macduff has just learned that his wife and children have been slaughtered and Malcolm has had to brace him up from his despair and tell him to use it to fuel his action against Macbeth
Be this the whetstone of your sword: let grief Convert to anger; blunt
not the heart, enrage it.
Malcolm is telling Macduff that he should take comfort and solace in the avenging of those deaths.
You are right, every night sees a dawn, and that is what Malcolm is telling Macduff, that the night of his grief and sorrow may be long, but not so long that there is no end to it, and that that dawn begins with bringing Macbeth down.
I would interpret the line about the night in much the same way as the proverb ‘it’s a long road that knows no turning’. Such an interpretation is in keeping with Aphorisms from Shakespeare Longman, Hurst, Rees, Orme, and Brown, 1812 entry 2913 ‘Patience and Hope’: which quotes the lines about cheer and night, adding as a footnote
Equivalent in sense to this sublime Allegorical Aphorism, but how different in Expression is the common Proverb - “‘Tis a long Lane which has no turning.”
The proverb also seems to puzzle people and you will find many discussions and variations for its interpretation. However, the explanation which best satisfies the ‘long night that never finds the day’ situation in Macbeth is that offered in the Oxford Dictionary of Proverbs
Commonly used as an assertion that an unfavourable situation will eventually change for the better.
I’m afraid I can go no further with citations on exactly why it means that, but would speculate that if the road is a metaphor for life, it will seem long and dreary if nothing ever changes. For Shakespeare’s version, night seems endless if there is no glimmer of dawn, and Macduff and Malcom are the ones who must clear the darkness away.