Is it possible to write "I'm hungry and tired" (我饿了，我也累了) with a single change-of-state 了?
The only thing wrong with "我饿了，我也累了。" is the second 我 is redundant. 

"我饿了，也累了。" is perfectly grammatical

You can also use  the [又 X 又 Y + 了] structure

Example: 我已經又累又饿了 (I am hungry and tired already)