A Guest's query about this song on another thread sparked my interest in this song. As a result, I published a post on my cultural blog about "One Solja Man". Here's a link to that post:

http://pancocojams.blogspot.com/2012/07/caribbean-song-one-solja-man.html Caribbean Song "One Solja Man"

That post includes a video of the song "One Solja Man". Here are my comments about that song with a hat tip to Q for his posting of those lyrics on this thread from the 1951 book by

The composer of this old Caribbean song is unknown. I believe "One Solja Man" is a Mento from Jamaica.

With regard to the words "no tear i jeremiah" found in the song "One Solja Man" song as found in that 1951 book Folk Songs of Jamaica edited by Tom Murray, Oxford University Press:

I believe "no tear i" means "don't wheel & turn me [spin me around] so fast [or "too fast"] or I might fall on the dance floor*.

A subsequent verse of that song refers to the Caribbean dance movement of "wheel and turn" and I believe that "tear" is another way of referring to that fast spinning around movement....

*I've given "tambourina" the general translation of "dance floor" instead of the specific translation of the musical instrument "tamborine".

That said, it's also my position that the "no tear I Jeremiah" lyrics are an adaptation - albeit for a different purpose and with a different meaning- of the words of Jeremiah 9, verses 1-18.   
Here are two verses from that chapter:

Jeremiah 9:1 - 1 "Oh, that my eyes were a fountain of tears; I would weep forever! I would sob day and night for all my people who have been slaughtered"

Jeremiah 9:18 - 18 "Quick! Begin your weeping! Let the tears flow from your eyes"

-snip-
Because of those verses and other verses in that book of the Bible, "Jeremiah" is now known as the "weeping prophet".

By the way, I found those verses and other verses of Jeremiah 9 to be particularly poignant in the context of the horrific massacre of movie attendees that occurred on July 20, 2012 in Aurora, Colorado.

Click http://pancocojams.blogspot.com/2012/07/caribbean-song-one-solja-man.html President Obama's Comments "The Dark Knight Rises" Shooting Aurora Colorado (Video & Transcript) for a post on my cultural blog about that massacre.

Best wishes,

Azizi Powell