The Honeyeaters and Australian Chats are a large and diverse family of small to medium-sized birds most common in Australia and New Guinea, but also found in New Zealand and certain Pacific Islands. Several genera display hybridization.
Gavicalis
Varied Honeyeater (Gavicalis versicolor) and Mangrove Honeyeater (G. fasciogularis) are interbreeding along a narrow hybrid zone near Townsville (eastern Australia). There is some gene flow from Varied into Mangrove Honeyeater (Joseph et al., 2019).

Varied Honeyeater © Jss367 | Wikimedia Commons
Lichenostomus
The Helmeted Honeyeater (Lichenostomus melanops cassidix) is critically endangered and could be ‘genetically rescued’ by the closely related subspecies L. m. gippslandicus. Harrisson et al. (2016) found that gene flow from gippslandicus to cassidix has declined substantially relative to pre-1990 levels and argue that natural levels of gene flow between the two subspecies should be restored.

The critically endangered Helmeted Honeyeater (Lichenostomus melanops cassidix)
Manorina
Examination of phenotypic variation of Black-eared Miner (Manorina melanotis) and Yellow-throated Miner (M. flavigula) revealed that these species were separable until 1950, when extensive habitat modification took place. After this event, the two taxa show a continuum of phenotypic traits between them, indicating hybridization (Clarke, Gordon & Clarke, 2001).

Black-eared Miner (Manorina melanotis) and Yellow-throated Miner (M. flavigula)
Melidectes
Two subgroups of honeyeaters of the Melidectes leucostephes – belfordi group are allopatric in New Guinea, but interbreed in a broad contact zone in the mountains of central New Guinea (Gilliard, 1959; Mayr & Gilliard, 1952).

Belford’s Honeyeater (Melidectes belfordi)
Myzomela
The Sooty (Myzomela tristami) and Cardinal Myzomela (M. cardinalis) recently came into secondary contact on the Solomon Islands. A genetic study reported nuclear introgression from the native species (M. tristami) to the colonizing species (M. cardinalis) (Sardell & Uy, 2016).

Cardinal Myzomela (M. cardinalis)
Phylidonyris
Putative hybrids between New-Holland Honeyeater (Phylidonyris novaehollandiae) and White-cheeked Honeyeater (P. niger) has been reported (Dabb, 2016; Groom, 2019).
References
Clarke, R. H., Gordon, I. R. & Clarke, M. F. (2001). Intraspecific phenotypic variability in the black-eared miner (Manorina melanotis); human-facilitated introgression and the consequences for an endangered taxon. Biological Conservation 99, 145-155.
Dabb, G. (2016) The observing of a first-generation hybrid honeyeater, and the appearance of second-generation hybrids. Canberra Bird Notes 43, 206-217.
Gilliard, E. T. (1959). The ecology of hybridization in New Guinea honeyeaters (Aves). American Museum novitates; no. 1937.
Groom, G. N. (2019). A photographic record of a possible New Holland Honeyeater Phylidonyris novaehollandiae longirostris × White-cheeked Honeyeater P. niger gouldii hybrid. Australian Field Ornithology, 36.
Harrisson, K. A., Pavlova, A., da Silva, A. G., Rose, R., Bull, J. K., Lancaster, M. L., Murray, N., Quin, B., Menkhorst, P., Magrath, M. J. L. & Sunnucks, P. (2016). Scope for genetic rescue of an endangered subspecies though re-establishing natural gene flow with another subspecies. Molecular Ecology 25, 1242-1258.
Joseph, L., Drew, A., Mason, I. J., & Peters, J. L. (2019). Introgression between non-sister species of honeyeaters (Aves: Meliphagidae) several million years after speciation. Biological Journal of the Linnean Society, 128(3):583-591.
Mayr, E. & Gilliard, E. T. (1952). Altitudinal hybridization in New Guinea honeyeaters. Condor, 325-337.
Sardell, J. M. & Uy, J. A. (2016). Hybridization following recent secondary contact results in asymmetric genotypic and phenotypic introgression between island species of Myzomela honeyeaters. Evolution 70, 257-269.