I agree it is nonsense. Convince the Catholic Church.
Honest question: who do you mean, in particular? "Church" has a lot of overlapping meanings, and when people make a short comment like this, what they seem to envision is "the Church" as monolith. Do you mean "define this as a doctrine"?
As to the doctrine, it does not seem the Church needs convincing, because the Church upholds private property, which is the basis (or one of the bases) of capitalism.
See Catechism #2401-2414 (Link).
(That's a lot of context, but Catholic doctrine is strongly dependent on these contexts, these interlacings of rights and duties.)
As to her leadership, the papacy and the Fathers and Doctors of the Church have been on record against Mammon (with the usual tug-o-war between "practicing" and "preaching") for 2000 years, and against Marxism for about 160.
I'd like to convince a LOT of Catholics of the dignity and the moral necessity of free enterprise. But is that what you mean by "convince the Church"?
Please excuse me if I am being unnecessarily obscure. (It's been a long day) What I'm getting at, is that all I have to convince the Church of, is Catholicism.