Are there any supplications or legitimate (Shar'i) ways to recover a gold set that a colleague denied possessing, and to make her return what she took?

You must remind your relative about lending her the jewelry, and if she insists on denying it, accuse her of betraying the trust and warn her of God's punishment, for He is the Knower of the Unseen. If she does not desist, report her to the authorities, and if you have evidence, present it. There is no specific supplication for retrieving that which is denied.