In addition to the grammatical reasons outlined by Barth, I'd like to point out a difference in meaning:
"Die Rechnung ist noch nicht geschrieben worden." would be used to indicate that the invoice has not, yet, been written. Just stating that it was not written, period.
"Die Rechnung konnte noch nicht geschrieben werden." would be used to indicate that one would have wanted to write the invoice, but that for some reason it has not, yet, been possible. The sentence would include a hint of an excuse, indicating that one is somewhat sorry for the fact, that it hasn't been written, yet.