Hausa Ajami (Hausa written in Arabic script) remains severely under-resourced for computational morphology. We present AjamiMorph, a zero-annotation framework that discovers morphemes through consensus among three unsupervised methods, namely, Byte Pair Encoding (BPE), transition-based boundary detection using Pointwise Mutual Information (PMI), and computational linguistics based Distributional Affix Mining (DAM). Using a Hausa Ajami Bible corpus consisting of 637,414 tokens, AjamiMorph identifies 1,611 high-confidence morphemes, achieving 99.9% coverage. The inventory exhibits a linguistically realistic distribution (66.0% stems, 22.6% suffixes, 11.4% prefixes) and recovers 77.8% of known Hausa affixes. A permutation test that shuffles method assignments (preserving per-method selection sizes) confirms that the observed agreement is above-chance; chi-square remains as a secondary check. A lightweight 5-gram LM comparison (characters vs. consensus morphemes) provides an extrinsic signal. We also report negative results for script-driven Arabic assumptions and LLM-first annotation. This work provides the first unsupervised morpheme inventory for Hausa Ajami and demonstrates consensus as a robust strategy for zero-resource morphology.