The currently widely accepted view is that both Psylloborini and the erstwhile Halyziini are nested inside Coccinellini, and hence synonymous with the last-mentioned.

Here are three recent and thorough phylogenetic studies that support this viewpoint:

Escalona HE, Zwick A, Li H-S, Li J, Wang X, Pang H, Hartley D, Jermiin LS, Nedvěd O, Misof B, Niehuis O, Ślipiński A, Tomaszewska W (2017) Molecular phylogeny reveals food plasticity in the evolution of true ladybird beetles (Coleoptera: Coccinellidae: Coccinellini). BMC Evolutionary Biology 17:151. 11 pages + Additional files. doi:10.1186/s12862-017-1002-3.

Che, LiHeng, Peng Zhang, ShaoHong Deng, Hermes E. Escalona, Xingmin Wang, Yun Li, Hong Pang (2021) New insights into the phylogeny and evolution of lady beetles (Coleoptera: Coccinellidae) by extensive sampling of genes and species. Molecular Phylogenetics and Evolution 156: 107045. doi:10.1016/j.ympev.2020.107045.

Tomaszewska W, Escalona HE, Hartley D, Li J, Wang X, Li H‐S, Pang H, Ślipiński A, Zwick A (2021) Phylogeny of true ladybird beetles (Coccinellidae: Coccinellini) reveals pervasive convergent evolution and a rapid Cenozoic radiation. Systematic Entomology 46(3): 611–631 + Suppl. Figs 1–6 + Suppl. Tables 1–6. doi:10.1111/syen.12479.