The Cuculiformes are represented by the Cuculidae (cuckoos). The phylogeny is not particularly well founded, and the divergence times are still mostly obscure:

Provisional genus-level phylogeny of extant Cuculidae following Nordén et al. (2023), with the distribution of each taxon being indicated by the colour-code used throughout this website (Distribution code). Available divergence times (Crotophaga + Geococcyx) + (Centropus + (Cuculus + Ceuthmochares + Piaya))) follow Stiller et al. (2024). [Chronotaxonomics would elevate current subfamilies to families. Cuculinae might have to be split into 2-3 families.]

Genus-level classification of extant Cuculidae.

References

Burleigh JG, Kimball RT, and Braun EL (2015), Building the avian tree of life using a large-scale, sparse supermatrix, Mol. Phylogenet. Evol. 84, 53-63. (abstract) 

Hackett SJ, Kimball RT, Reddy S, Bowie RCK, Braun EL, Braun MJ, Chojnowski JL, Cox WA, Han KL, Harshman J, Huddleston CJ, Marks BD, Miglia KJ, Moore WS, Sheldon FH, Steadman DW, Witt CC, and Yuri T (2008), A phylogenomic study of birds reveals their evolutionary history, Science 320, 1763-68. (abstract)

Hughes JM (2003), Phylogeny of cooperatively breeding cuckoos (Cuculidae, Crotophaginae) based on mitochondrial gene sequences, Naturwissenschaften 90, 231-233. (abstract)

Hughes JM (2006), Phylogeny of the cuckoo genus Coccyzus (Aves: Cuculidae): A test of monophyly, Syst. Biodiv. 4, 483-488. (abstract)

Johnson KP, Goodman SM, and Lanyon SM (2000), A phylogenetic study of the Malagasy Couas with insights into cuckoo relationships, Mol. Phylogenet. Evol. 14, 436-444.  (pdf)

Nordén KK, Cooney CR, Babarovic F, and Stoddard MC (2023), Historical contingency influences the diversity of feather nanostructures in cuckoos, bioRxiv [preprint]. (pdf)

Prum RO, Berv JS, Dornburg A, Field DJ, Townsend JP, Lemmon EM, and Lemmon AR (2015), A comprehensive phylogeny of birds (Aves) using targeted next-generation DNA sequencing, Nature 526, 569-57. (abstract)

Qu J, Cong J, Guo C, Hou J, and Shi B (2017), Complete mitochondrial genome of the Greater Coucal, Centropus sinensis (Aves: Cuculiformes), Mitochondrial DNA Part A 28, 311-312. (abstract)

Sorenson MD, and Payne RB (2005), Molecular systematics: cuckoo phylogeny inferred from mitochondrial DNA sequences in "The Cuckoos", pp. 68-94 (R.B. Payne, ed.). Oxford University Press, Oxford. (abstract)

Stiller J, Feng S, Chowdhury AA, Rivas-González I, Duchêne DA, Fang Q, Deng Y, Kozlov A, Stamatakis A, Claramunt S, Nguyen JMT, Ho SYW, Faircloth BC, Haag J, Houde P, Cracraft J, Balaban M, Mai U, Chen G, Gao R, Zhou C, Xie Y, Huang Z, Cao Z, Yan Z, Ogilvie HA, Nakhleh L, Lindow B, Morel B, Fjeldså J, Hosner PA, da Fonseca RR, Petersen B, Tobias JA, Székely T, Kennedy JD, Reeve AH, Liker A, Stervander M, Antunes A, Tietze DT, Bertelsen M, Lei F, Rahbek C, Graves GR, Schierup MH, Warnow T, Braun EL, Gilbert MTP, Jarvis ED, Mirarab S, and Zhang G (2024), Complexity of avian evolution revealed by family-level genomes, Nature 629, 851-860. (pdf)

Tian Y, Xu J, Dou L, Zheng A, Qiao L, Xie j, and Zhang X (2021), The complete mitochondrial genome of the Indian Cuckoo Cuculus micropterus (Aves: Cuculiformes), Mitochondrial DNA Part B 6, 2556-58. (pdf)

Wang N, Liang B, Huo J, and Liang W (2016), The complete mitochondrial genome and the phylogenetic position of the Lesser Cuckoo, Cuculus poliocephalus (Aves: Cuculiformes), Mitochondrial DNA Part A 27, 4409-10. (abstract)