Here's what I found one one:

TICKETY-BOO
The usual meaning ... that something is satisfactory, all in order, or OK.

We can't be sure what its origin is. Eric Partridge always contended that the word was forces' slang, most probably from the Royal Air Force, and that it dates from the early 1920s or thereabouts (though the Oxford English Dictionary doesn't find a written example before 1939).

The difficult bit is taking the word back any further than the 1920s. It could combine "that's the ticket" (with much the same sense)with the childish phrase "peek-a-boo". But some find a link with the British Army in India, suggesting it comes from the Hindi phrase tikai babu, which is translated as "it's all right, sir".

My money would be on the second suggested origin.