Green’s Dictionary of Slang

gravy train n.

[gravy n. (2) + SE train; Dillard, Lexicon of Black English (1977), suggests the image of a gambler who is in the ‘gravy’ and thus pursued by a ‘train’ of those who wish to benefit]

(orig. US) a sinecure, a simple, substantially profitable situation from which one can benefit easily; thus ride the gravy train

Connellsville (PA) Courier Nov. n.p.: Johnston claims that Reuben Nelson and another tall negro were in New Haven the night of the escape and that they broke into the lockup. Johnston further states that the next day Kelson laughingly told him that the New Haven lockup was ‘a gravy train.’.
[US](con. 1914–18) L. Nason Three Lights from a Match 139: ‘All you men, git!’ he roared. ‘Up on the lines, now, every one. The gravy train is ditched.’.
[US]T. Thursday ‘Good Luck is No Good’ in Federal Agent Nov. [Internet] I ain’t worked around Panama for nearly six years. That’s where the gravy train runs for me.
[US]B. Schulberg Harder They Fall (1971) 154: He had really caught the gravy train this time.
[US]C. Himes Crazy Kill 137: She killed her legal husband to keep him from fouling up her little gravy train.
[UK]T. Rhone Old Story Time I i: With financing, ABC could be a gravy train, a money machine.
[UK]T. Blacker Fixx 177: Charming old duffer [...] attempts to jump property gravy train.
[UK]Indep. Rev. 30 June 4: Jacques Santer is queuing to buy a ticket on the Euro gravy train.
[NZ]A. Duff Jake’s Long Shadow 73: We know you’re on the gravy train of help-a-Maori-in-prison, when it’s really help the Maori send the stupid govmint another invoice for services rendered.
[UK]Sun. Times Sport 19 Dec. 5: [headline] Barca Board Gravy Train.

In phrases

ride the gravy train (v.) (also ride a gravy train, ...the gravy boat)

(US) to enjoy a comfortable life; thus gravy-riding n.

[US]S.V. Benét Young People’s Pride 17: When you haven’t any money you can’t go to parties in New York unless you raise gravy riding to a fine art.
[US]Buckner ‘Ranch Diction of the Texas Panhandle’ in AS VIII:1 32: ride a gravy train. To continue to receive more than one’s deserts.
[US]Monteleone Criminal Sl. (rev. edn).
[US]J. Jones From Here to Eternity (1998) 53: SD men and jockstraps are all the same, fugitives from straight duty. They ain’t got what it takes so they ride the gravytrain.
[US]M. Puzo Godfather 147: I’ve been riding the gravy train all my life, it’s about time I paid my dues.
Mail & Guardian Online (SA) [Internet] It is the hypocrisy of this ANCWL (a bunch of sycophantic gravy train riders who simply kowtow to their masters bidding).
[UK]Indep. on Sunday 25 Oct. [Internet] His job pays well in money and in gravy-train riding ‘benefits’.