Several options, all of which sound very antiquated but are probably grammatically acceptable:
Option 1 - Did they specify that the sentence had to be a standalone and understandable paragraph? Because if it were permitted to use it as the beginning of a second sentence, you could easily do something like this, albeit it's antiquated English:
"After Dairyman Wilson had separated the group, he called all of the farmhands between the ages of 18 and 25 to follow him into the fields. Them he gathered by the foot of the old oak tree."
"John and Iona are expected to perform, but not the others. Them, we do not expect to perform."
Option 2: consider this passage from the King James Bible (Matthew 13:12):
"For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath."
Now consider that an analogue of this sentence written to refer to groups of people in the plural, rather than individuals in the singular, and with the meaning changed slightly (for purely illustrative purposes) could be written something like this:
"Them, unto whom much has been given, shall be given more. But those who have not, from them shall be taken away even that they hath."
I'm pretty sure this (or a similar construct) would be acceptable.
Option three: alter the sentence structure of a sentence involving the word "them" and insert a "whom" - e.g., instead of saying:
"We went to the shop with them and they bought a packet of cheerios,"
You could say:
"Them, with whom we went to the shop, bought a packet of cheerios."
I mean, people would think you had just stepped out of the pages of a Thomas Hardy novel, but it would technically be correct. I think.