I believe it would almost certainly be Tim Kaine as the consensus candidate given that he's the only other person thats actually received the nominating votes of the entire convention. Anybody else would be extremely contentious, whereas it would be hard to argue if they just elevated Kaine to the position he's already been vetted for. It's literally his primary duty---it just happened much earlier than expected. I can't imagine the DNC would put anyone else on the ticket, he'd be the memoriam candidate fighting to uphold her legacy.
I'd be more interested in seeing who they selected as the VP since they wouldn't have much time to do any vetting.
In case you're interested these are the rules the DNC uses to select a replacement:
Article 2, section 1 of the Rules and Bylaws of the Democratic Party states that the DNC has the authority to fill vacancies in the nominations for president and vice president. "The Democratic National Committee shall have general responsibility for the affairs of the Democratic Party between National Conventions, subject to the provisions of the Charter and to the resolutions or other official actions of the National Convention. This responsibility shall include, but not be limited to ... Filling vacancies in the nominations for the office of the President and Vice President," reads Article 2.1(c).
Article 2, section 7 states, " a special meeting to fill a vacancy on the National ticket shall be held on the call of the Chairperson, who shall set the date for such meeting in accordance with the procedural rules provided for in Article Two, Section 8(d) of these Bylaws." Article 2, section 8(d) reads, "all questions before the Democratic National Committee shall be determined by majority vote of those members present and voting in person or by proxy."
https://ballotpedia.org/State_laws_and_party_rules_on_replacing_a_presidential_nominee
I also think that in these circumstances (whether it was Trump or Clinton) many courts, if not most courts, would be willing to toss the ballot access laws and that even more state legislatures (if not all) would extend their deadlines to meet this extraordinary occurrence and prevent a one party election.