Formal:
* Assert: To state something confidently, even if it might not be true.
* Claim: To state that something is true, often without proof.
* Declare: To state something formally or officially.
* Maintain: To continue to state something, even if challenged.
Informal:
* Say: To express something verbally.
* Claim: To state something as true, often with little evidence.
* Charge: To accuse someone of something.
* Accuse: To say that someone has done something wrong.
* Imply: To suggest something indirectly.
Legal:
* Aver: To state something as a fact in a legal context.
* Charge: To formally accuse someone of a crime.
The best synonym for "allege" will depend on the specific situation and the nuance you want to convey.