Cyanosis in the setting of normal O2 sats suggests methemoglobinemia. It'd be interesting to see what this kid's blood looked like (chocolate brown?) and whether it changed color in response to oxygen -- if not, you've got a likely candidate.
If blood tests do reveal an increased percentage of methemoglobin, you've got to consider whether it's congenital or acquired. A careful history might help you out, including a detailed family history, since congenital cases often run in families (hemoglobin M--autosomal dominant; cytochromeb5/cb5 reductase deficiency--autosomal recessive or compound heterozygous).
The two acute episodes argue against a congenital form, but you could be dealing with heterozygous cb5 reductase deficiency + acute stressor. You'd want to ask about recent medications, toxin exposures, and the source of drinking water (since nitrates in well water can cause this). There have been case reports of methemoglobinemia in kids who eat crayons: some of them contain aniline dyes, which are a well-known cause of methemoglobinemia. The recent illness is intriguing -- what was it? Sometimes acute methemoglobinemia follows diarrheal illnesses, for reasons that are still debated.
If the blood does change colour in response to oxygen, you might be thinking of a low-oxygen affinity hemoglobin, or a pulmonary or cardiac cause (which would imply that the O2 sat reading was wrong and the CXR was deceptive). Raynaud's is an interesting suggestion, but you'd expect a clear history of cold exposure, sharply demarcated colour change, and no cyanosis of the lips. There's a similar condition called acrocyanosis -- blue hands and feet caused by vasospasm, sometimes stress-induced, but from what I know it's usually seen in adults, more common in women, and doesn't cause blue lips.
