From The Cincinnati Lancet-Clinic. Cincinnati: J.C. Culbertson, 1886, page 200:

JUS' KEEP ON KEEPIN' ON.

If the day looks kinder gloomy an' your chances kinder slim :
If the situation's puzzlin' an' the prospect awful grim,
An' perplexities keep pressin' till all hope is nearly gone,
Jus' bristle up and grit your teeth, an' keep on keepin' on.

Fumin' never wins a fight an' frettin' never pays ;
There ain't no good in broodin' in these pessimistic ways —
Smile jus' kinder cheerfully when hope is nearly gone.
An' bristle up, and grit your teeth, an' keep on keepin' on.

There ain't no use in growlin' an' grumblin' all the time
When music's ringin' everywhere, an' everything's a rhyme —
Jus' keep on smilin' cheerfully, if hope is nearly gone,
An' bristle up an' grit your teeth, an' keep on keepin' on.

— New Orleans Times-Democrat.