In the search of new inhibitors for human coronavirus (HCoV), we screened extracts of endemic Annonaceae plants on an assay using a cellular model of Huh-7 cells infected with the human alphacoronavirus HCoV-229E. The EtOAc bark extract of the rare Southeast Asian plant Neo-uvaria foetida exhibited inhibition of HCoV-229E and SARS-CoV-2 viruses with IC50 values of 3.8 and 7.8 μg/mL, respectively. Using LC-MS/MS and molecular networking analysis guided isolation, we discovered two new labdane-type diterpenoids, 8-epi-acuminolide (1) and foetidalabdane A (4), and three known labdane diterpenoids, acuminolide (2), 17-O-acetylacuminolide (3), and spiroacuminolide (5). A new norlabdane diterpene, 16-foetinorlabdoic acid (6), was also isolated and identified. Excluding compounds 5 and 6, all other metabolites were active against the virus HCoV-229E. Terpenoids 1 and 4 presented antiviral activity against SARS-CoV-2 with IC50 values of 63.3 and 93.5 μM, respectively, indicating lower potency. Additionally, virological assays demonstrated that compounds 1, 2, and 3 exert antiviral effects against Zika virus by specifically interfering with the late stage of its infectious cycle with IC50 values of 76.0, 31.9, and 14.9 μM, respectively.