I sang this at a funeral a year ago (2019), by request. What I sing comes from the Ken Stubbs collection thin book The Life of a Man (EFDS 12/6d) though I sang (as requested) the well known melody rather than that in the book which I prefer. I'm sure I changed some words here and there.
That service was in the Reformed Church that the deceased attended regularly.
The song mentions churchyards but not belief.

Collected from Harry Holman, Copthorne Surrey
Fingers crossed for us all, April 2020.

As I was a-walking one morning at ease,
A-viewing the leaves as they hung from the trees,
They were all in full motion or appearing to be
And those that were withered, they fell from the tree

(Then what is the life of a man, any more than the leaves,
A man has his seasons, so why should he grieve;
Even though in this wide world he appears bright and gay,
Like the leaves we shall wither and soon fade away)

Did you not see the leaves but a short time ago?
They were all in full motion appearing to grow,
When the frost came upon them and wither'd them all,
Then the rain came upon them and down they did fall

(Chorus)

If you go down to yonder churchyard, many names there you'll see
Who have fallen from this world like the leaves from the trees;
What with age and affliction upon us all,
Like the leaves we shall wither and down we shall fall.

(Chorus)