The source should be no earlier than 2009. Is it right？
“The source should be no earlier than 2009“.
"The earliest data source I accept only can be in 2009"

Are they right？
Any better sentence?

Question

The source should be no earlier than 2009. Is it right？
“The source should be no earlier than 2009“. 
"The earliest data source I accept only can be in 2009"

Are they right？
Any better sentence?

Answer

The source should have originated no earlier than 2009

Answer

No sources older than 2009 will be accepted.
Only use sources newer than 2009.

Your second sentence uses more words than necessary, and the first sounds awkward. But of the two, your first sentence was very close. There are many ways to say this.