"Praise Him, Praise Him"

Near the end of last year, I was thinking about "Praise Him, Praise Him," which - if I remember aright - I learned in Sunday school many years ago.  According to hymnary.org, the text is anonymous and in the public domain:

Praise Him, praise Him,
Praise Him in the morning,
Praise Him in the noontime.
Praise Him, praise Him,
Praise Him when the sun goes down.

Subsequent verses simply replace "praise" with an-other verb:  "love," "trust," and "serve."  (Hymnary.org also has a fifth verse that replaces "Praise Him" with "Jesus," although I don't remember singing that one.)

The first verse, at least, seems to come from a number of Psalms.  Psalm 148:1-4 also has this repeated "Praise Him," as does the entirety of Psalm 150.  The range of temporal elements ("in the morning... in the noontime... when the sun goes down") is something of a merism, and it seems to come from Psalm 113:3:  "From the rising of the sun to its setting, the name of the LORD is to be praised!"

Hymnary.org doesn't have a melody, but from what I remember, it's something like:

The "sun goes down" part of the line "Praise Him when the sun goes down" is sung to a descending group of notes (B A G in my notation), musically giving a sense of that "go[ing] down."