I'm completely honest with my Dad about where I get my information. I have told him one of my sources is the Internet but other sources are the WTS publications and he is free to look up what we talk about. Due to his advancing age, he's kind of stuck with me as I'm the only family member actively engaged with him at the moment. So he's kinda stuck with me. I don't think he minds... he tells me he misses me when I can't get up to see him.
If my Dad wants to talk about religious things, my strategy is to choose topics which cannot be refuted. The 2 main topics of discussion lately are:
1) The complete lack of arrival of Armaggeddon.
Every time he says to me "They're saying it's real close." (in my mind I say to myself "Who is this 'they' he keeps talking about? It's YOU man... YOU! Own up to it!" but what I actually say is....) "Dad, they've been saying this for over 130 years and it hasn't arrived yet. 130 years isn't close, Dad. When you say it's close and close doesn't happen, you lose credibility." That usually ends the conversation
2) The pedophilia going on within the organization.
Since there was a pedophile in his previous congregation and it became public news, he cannot turn a blind eye to the fact that this is going on. I know it bothers him (which is good!). And because it was in his own congregation, it makes it a personal thing. He can't refute that this abuse goes on because it is regularly in the news as well. I pointed out to him not long ago that the WTS has bad mouthed Catholics for years about the exact same problem going on in their own organization. And it's still happening.