The New Linguistic and Exegetical Key to the NT has something similar: "The word is used [in 2Cor 9:13] specifically to introduce or express a conviction; i.e. the obj. confession which especially has reference to confessing Christ or the teaching of his church."
The NAC-2 Corinthians commentary (p.414) has this:
The gift is also part of their confession of the gospel of Christ. The "obedience of your confession" could be a [1] subjective genitive, "obedience created by your confession"; [2] an objective genitive, "obedience to your confession"; [3] or a genitive of apposition, "the obedience which is one's confession." The first option seems best. Confession is to be more than the mouthing of pious cliches; it should lead to actions that speak louder than words.
[End quote. Bracketed material is Bobcat's for clarity.]
The rNWT rendering does seem to be a bit anomylous, though, by putting "as you publicly declared" in a separate phrase. The rNWT rendering also turns homologias (a noun) into a verb. The phrase is literally τῇ ὑποταγῇ τῆς ὁμολογίας ὑμῶν ("the submission [noun] of the confession [noun] of you").
Leaving_Quietly makes a good point that the WT maintains a different lingo from the churches. For the WT, "confession" usually only refers to repenting from sin.
Alternate renderings can be found here.
Bobcat