The complete conversation is as follows and as is evidenced Tyrion is mainly worried about carrying on the succession he isn't proposing anything yet. He implies that a democratic solution could be an answer by suggesting the Night's Watch's elections and the Ironborns Kings Moot but get's cut off before he can complete the sentence. Tyrion hasn't actually suggested anything he is just worried about the succession continuing and even if he has a suggestion Dany wouldn't hear it.
Tyrion Lannister: Because I believe in you and the world you want to build. But the world you want to build doesn't get built all at once. Probably not in a single lifetime. How do we ensure your vision endures? After you break the wheel, how do we make sure it stays broken?
Daenerys Targaryen: You want to know who sits on the Iron Throne after I'm dead?
Tyrion Lannister: You say you can't have children. But there are other ways of choosing a successor. The Night's Watch has one method, The Iron born folk, although many flaws
Daenerys Targaryen: We will discuss the succession after I wear the crown.
Tyrion Lannister: Your Grace, I saw hundreds of arrows fly towards you when you fought on Blackwater Rush, and I saw hundred of arrows miss. But any one of them could have found your heart and ended you.
Daenerys Targaryen: You've been thinking about my death quite a bit, haven't you? Is this one of the items you've discussed with your brother in King's Landing?
Tyrion Lannister: I'm trying to serve you by planning for the long term.
Daenerys Targaryen: Perhaps if you'd planned for the short term, we wouldn't have lost Dorne and Highgarden. We will discuss the succession after I wear the crown.
Game of Thrones, Season 7 Episode 6, "Beyond the Wall"
However, the ending to Season 7 could have put Tyrion's mind at rest when he saw the potential for #BOATBABY. Though of course he seems to look more worried than happy about the situation.
An important point mentioned by @Anthony Grist in the comments is also relvant here. Just because he wanted to discuss the matter and start thinking about it right now doesn't mean he wants anything to happen straight away. For all we know Tyrion has no idea for what should happen with the succession but just wanted to open the discussion up so there was a possibility there.