How can we explain to the disbelievers when we claim that tiredness is a form of human weakness and cannot be attributed to Allah but anger can be attributed to Him?

It is according to its structure. Anger is an attribute but not a name. In one hadeeth the Prophet (ﷺ) speaks about Allah being Happy and in another Allah laughs but these are not names; angry one and laughing one.

The rule is that we establish what Allah establishes for Himself and as a general rule we negate any shortcoming from Allah.

Anger has been established by Allah and it need not be a weakness, where as getting tired, there is no other way in understanding it but weakness.