The Royal Order of Adverbs has already been discussed on ELU.
This example contains two adverbs of the same category (manner) but very different subcategories, because they're essentially modifying two different senses of count:
- to determine the total number in a set
- to enunciate that determining process [counting out]
Here, 'one by one' describes the way the summing is done, and 'out loud' shows that sense (2) is in play. So the usual 'rule'
- When we use multiple adverbs of the same category to modify the same verb, we order them based on how specific the information is that they provide.
does not apply. The 'manners' described are orthogonal.
However, 'counting out', often used in primary schools, shows a large degree of cohesion between 'count' and 'out [loud]'. This adverbial needs to be close to the verb, as others have commented.
A complication is that 'count' sounds off when separated from the direct object.
A reasonable compromise, as FumbleFingers suggests, is
- I counted my classmates out loud, one by one.
The comma is at least preferable to echo the pause most would leave between the adverbials. It helps with parsing, and is in line with the comma between coordinate adjectives.