The correct form is ‘more tired.’ In English, we typically use ‘more’ with adjectives that have two or more syllables, and ‘tired’ has two syllables. While the word ‘tireder’ might sound logical, it is not considered standard usage in English.
The structure for comparative adjectives in English usually follows the rule of using ‘more’ before adjectives that are longer, which helps to form the comparative. For example, we say ‘more beautiful’ instead of ‘beautifuller’ and ‘more interesting’ rather than ‘interestinger.’
In summary, the appropriate way to express a greater level of tiredness is by saying ‘more tired’ instead of ‘tireder.’