Similar meaning, but slightly more formal:
* Scarcely
* Hardly
* Slighly
* Just
* Merely
More emphatic:
* Only just
* With difficulty
* By a hair's breadth
* At the very least
More informal:
* Almost not
* Nearly not
* Close to not
Example:
* Original: She barely finished her homework on time.
* Replaced: She scarcely finished her homework on time.
* Replaced: She only just finished her homework on time.
* Replaced: She almost didn't finish her homework on time.
The best replacement will depend on the tone and specific meaning you want to convey.