Which doctrines are based solely on the apocrypha? What Roman Catholic doctrines are based only in the 7 books canonized by the Roman church, but not accepted by Protestants. (e.g., Tobit, Judith, Maccabees, the additions to Daniel and Esther, etc...)
There's a few notions, but no doctrine, as the domain of doctrine in the Catholic Church is encompassed entirely by the New Testament insofar as it is the fulfillment of the entire Old Testament. 

But, here's a sampling off the top of my head:


Tobit 

Archangel Rapahel in the heavenly host
Respect for burying the dead as a corporal work of mercy

Maccabees 

Understanding of the efficaciousness of praying for the dead.

Judith

Maybe a little to do with Just War Theory?

Wisdom

Deeper understanding of who Christ was/is and how He would be treated

Sirach

Love of wisdom personified (may have something to do with Mary's title "Seat of Wisdom")





Concerning the state of purgatory and Maccabees, Protestants wholly reject purgatory and they do so because they say it's only in Maccabees, which they also reject. But when Jesus says in His parable about repayment to the last penny, that also informs the Catholic understanding of what purgatory is.