While it's primarily the work of the Holy Spirit and God's grace acting with a person's free will that ultimately brings them to conversion, there are still a lot of things you can do to be God's instrument in this.
If they belong to evangelical churches, they may or they may not be happy where they are. In order to make them take fresh look at the Church from an objective standpoint, you have to clearly show them two things:
 That there is something that the Catholic Church posseses that they can't get anywhere else, even in a local church community to which they may have some emotional attachment. There are a number of things that fall under this category: The Eucharist and the other Sacraments as means of grace; the Church's historical origin in Christ as well as her historical continuity; an authoritative, Christ given authority to interpret the Scriptures in contrast to the multitude of personal, often conflicting biblical interpretations; the profundity of the liturgy; a unified and clear teaching voice on moral issues; and so on.
To this end, you should be ready to answer any questions they might have about the Catholic Faith (just because they were raised Catholic, you should not assume they know the rudiments of the Faith--in fact, the opposite is probably true since many Catholics drift away precisely because they do not know the Faith, or possess a very young child's understanding of it.). This doesn't mean you need to be an expert in theology, Scripture, Church law and apologetics, but you should at least be able to answer their basic questions. If you don't know something they ask about, don't be afraid to say "I don't know, but I'll look it up and get back with you," then do it.
 That they would gain all the things they have at their non-Catholic church but at the same time they would not be losing anything essential if they left there and returned to the Catholic Church. This might be a little tricky if they consider some un-essentials to Christianity itself --such as warm fellowship, good musicians, childcare during services, easy availability of Bible studies, dynamic preaching, etc -- to be absolutely essential. In that case, you'd have to show them how -- nice and helpful as these things are -- they do not comprise the essence of being a Christian -- that is, the grace found in the Sacraments, being in full communion with the Church body established by Christ, the holy example and solicitude of the Saints, and the fullness of truth found in Sacred Scripture and Sacred Tradition-- which can only be found in the Catholic Church. Having said that, it's also true that you often can find many of those nice non-essentials in many (though, admittedly, not all) Catholic parishes.
The above, and your own example of a holy, Christian life (with lots of prayer, their own honesty and openess to the truth, and God's grace) will bring them home. Hope that helps. :)