You cannot say a units.
You can say a constant 10 units, because you are talking about all 10 of those units as 1 indivisible thing. The real noun is something like "a group of 10 units that remain constant." Just like you can say a bushel of apples or a bag of coins.
Your second example doesn't work because you aren't just talking about a constant, but the full concept of "a constant 10 units."
Saying a bag of coins and a bag which is containing 10 coins very technically refers to the same thing, but a bag which is containing 10 coins makes it sound like you don't care about the coins at all and you really just want the bag.