Malayalam has been written in Arabic script (Arabi Malayalam) and Syriac script (Suriyani Malayalam), with significant extensions to both to deal with the large number of phonemes. The large number of phonemes means any Romanisation is going to involve either diacritics or digraphs; but there’s no intrinsic reason why Malayalam, or any other language, cannot be romanised; and Romanization of Malayalam – Wikipedia lists two ASCII and two scholarly romanisations.