Green’s Dictionary of Slang

a steady job, abbrev. SE situation.

1842		Wkly Rake (NY) 12 Nov. n.p.: Lunatics — Fellows jumping out of a ‘sit,’ by which they are making a very honest living [...] and into a station they were never intended for — that of publishers.
1895		Mirror of Life 20 July 2/2: [T]he bossing of this ‘cullud pusson’ soon became equal to a comfortable sit of at least a couple of thousand a year.
1914		Joyce Dubliners 91: Bu Hogan has a good sit, hasn’t he?