In a relatively informal correspondence, I'd use the phrasal verb 'put someone down for' : 'I'll put you down for next April 21st". 'I'll pencil you in for..' would have the same meaning, but it's a little more tentative, and suggests that this is subject to confirmation. 'Sign you up' would also work, but not 'sign in'. Another option is 'book you in', which sounds rather less informal. Otherwise, 'register you for' is possible, but less idiomatic. Two other points: Is 'conversation' the right word? Perhaps 'debate' or 'discussion'? Also, note that it's join + object, not join in i.e. 'join our debate.' Also, 'are' is better than 'were' in the second line.

I'd add to SuKi's answer that "in due course" sound very formal. I'd leave it out unless you are going to delay sending out the invitation for some time. Then I'd say something like "in a few weeks" or whatever the time interval is.