A series of 6-amino-4-substituted-3-methyl-2,4-dihydropyrano[2,3-c]pyrazole-5-carbonitriles 5a–j were synthesized via one-pot, four-component condensation reactions of aryl aldehydes 1a–j, propanedinitrile (2), hydrazine hydrate (3) and ethyl acetoacetate (4) under solvent-free conditions. We report herein the use of the Brønsted acid ionic liquid (BAIL) triethylammonium hydrogen sulphate [Et3NH][HSO4] as catalyst for this multi-component synthesis. Compared with the available reaction methodology, this new method has consistent advantages, including excellent yields, a short reaction time, mild reaction conditions and catalyst reusability. Selected synthesized derivatives were evaluated for in vitro anticancer activity against four human cancer cell lines viz. melanoma cancer cell line (SK-MEL-2), breast cancer cell line(MDA-MB-231), leukemia cancer cell line (K-562) and cervical cancer cell line (HeLa). Compounds 5b, 5d, 5g, 5h and 5j exhibited promising anticancer activity against all selected human cancer cell lines, except HeLa. Molecular docking studies also confirmed 5b and 5d as good lead molecules. An in silico ADMET study of the synthesized anticancer agents indicated good oral drug-like behavior and non-toxic nature.