If Stonecoil Serpent's X is 0, it enters the battlefield as 0/0 with no +1/+1 counters on it, and The Great Henge's ability will trigger, but Stonecoil Serpent will go to the graveyard as a state-based action for having a toughness of 0 (C.R. 704.5f), and this will happen even before that ability goes to the stack, let alone gets to resolve (C.R. 704.3, 117.4, 117.5). Even though that ability will still get to resolve (C.R. 113.7a), Stonecoil Serpent won't be there anymore for you to put a +1/+1 counter on by the time it resolves (C.R. 400.7; see also this thread).
Compare The Great Henge with Master Biomancer or Metallic Mimic, which give certain creatures additional +1/+1 counters right as they enter the battlefield. Unlike with these two, The Great Henge's last ability is a triggered ability which doesn't do anything right when it triggers (C.R. 603.2).
I knew that if I created a 1/1 Serpent that the Henge would make it a 2/2 and it wouldn't enable the Beast to attack.
I tried to create a 0/0 Serpent hoping the Henge would make it a 1/1. It didn't. The Serpent died as a 0/0 before the Henge could buff it.
Is there a way to do this legally? I played this match on Arena but I also play this deck in paper at FNM.
If Stonecoil Serpent's X is 0, it enters the battlefield as 0/0 with no +1/+1 counters on it, and The Great Henge's ability will trigger, but Stonecoil Serpent will go to the graveyard as a state-based action for having a toughness of 0 (C.R. 704.5f), and this will happen even before that ability goes to the stack, let alone gets to resolve (C.R. 704.3, 117.4, 117.5). Even though that ability will still get to resolve (C.R. 113.7a), Stonecoil Serpent won't be there anymore for you to put a +1/+1 counter on by the time it resolves (C.R. 400.7; see also this thread).
Compare The Great Henge with Master Biomancer or Metallic Mimic, which give certain creatures additional +1/+1 counters right as they enter the battlefield. Unlike with these two, The Great Henge's last ability is a triggered ability which doesn't do anything right when it triggers (C.R. 603.2).
EDIT (Jan. 29): Edited.