Frankfurt to Koblenz

There are direct trains departing Frankfurt’s airport and arriving in Koblenz 1h 15m later: https://int.bahn.de/en. The name of Frankfurt’s airport is Main (M) Flughafen.

The name of Frankfurt’s airport is Main (M) Flughafen.
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The name of the airport is "Frankfurt am Main Flughafen" or "Frankfurt(M) Flughafen". The (M) stands for Main, the name of the river Frankfurt is on, as compared to Frankfurt am Oder, a different Frankfurt.

I would definitely go by train. Look up schedules on the Bahn website.

Regional trains and S-Bahns leave from the close in Regionalbahnhof. There are direct (no change) Regional Expresses (RE) leaving from the Regionalbhf very two hours, at 9:24, 11:24, etc. Theygo via Bingen and take 1H30m. The standard fare is 33,20€ for one person (you didn't say how many are traveling with you). There are other regional train connections, such as taking an S-Bahn to Mainz or Wiesbaden and a direct regional train from there to Koblenz. Any regional connection following those routes to Koblenz will have the same fare.

You might be tempted to take a direct Intercity Express (ICE) in 1H13m, but the full fare for the ICE is 43,50€/P, hardy worth the extra price for 17 minutes. There are lower ICE fares with an advance purchase, but these tickets are train specific, i.e., valid only for a certain train on that date, and have to be purchased before the day of travel. If your flight is late arriving, you could lose the pre-purchased ticket and have to buy a new one.

Another fare option would be a Deutschland Ticket, which cost 25€/P for an entire calendar month, and it is valid for travel on all regional trains (so at 25€, so for a single person it would pay for itself going just to Koblenz). But you have to buy it online from the Bahn, and it is a subscription, which will renew for another 25€ every month if you don't cancel it by a certain time.

In 2017, I went from the airport to St Goar via Bingen. I beat the system by a little by buying an RMV (Frankfurt metro) ticket from the airport to Bingen (10,55€ today and a Bahn ticket from Bingen to St Goar (9,40€ today), 19,55€ vs 25,60€ for a Bahn ticket for the entire trip.

You could do the same thing today with a 10,55€ RMV Ticket to Bingen and an 18,70€ ticket from there to Koblenz, 29,25€ vs 33,20€ for a Bahn ticket for the entire trip. But you would have to use ticket automats in the FRA Regbhf or buy the tickets online.

To make sure you are taking the scenic route along the river, take the advice of The Man in Seat 61:
https://www.seat61.com/places-of-interest/rails-down-the-rhine.htm

All of the tickets with the 33,20€ fares will take the scenic route down the river. The connections via Mainz will go down the "left bank" via Bingen and Bacharach; the connections via Wiesbaden will go down the right bank, via Rüdesheim and St Goarshausen, then cross the river into Koblenz just past Braubach.

Do not, under any circumstances, take a boat. This is an un-scenic part of the Rhine, except maybe at Koblenz itself. The [really] "scenic Middle Rhine" runs roughly from Bingen to Boppard.

I think I would call the scenic part of the Rhine Bingen to St Goar. I've been on a boat several times between Bacharach and St Goar and once between Bingen and Bacharach. I've never been on a boat between St Goar and Boppard, but I have taken the train between St Goar and Boppard more than once, stayed in Boppard, and visited Bad Salzig, and I don't think that part of the Rhein can compare with Bingen to St Goar.

Thanks everyone for the responses (there will be two of us traveling)

For two people, 2 one way tickets from the airport to the Mainz Hbf, 2x 6,30€, plus a two person Rheinland-Pfalz-Ticket for 35,-€ = 47,60€, 23,80€/P. A Rheinland-Pfalz-Ticket is valid for any regional train in the state of Rheinland-Pfalz all day long, after 9 am.

Note: It doesn't matter what combination of trains you take. You can take the S-Bahn to Mainz (or Wiesbaden) or a regional train to anywhere in Rheinland-Pfalz, e.g., Ingelheim or Bingen) and any regional train from there to Koblenz. In Mainz you don't have to change trains, just tickets.

Now, 23,80€ is less than 25€, so this fare is better than the Deutschland-Ticket, but if you are using other trains in Germany, you should look at the Deutschland-Ticket.

Take the train from the airport. Know that the Deutsche Bahn is a disaster and that the train you take could be cancelled or delayed. It’s a part of life there.

Note the Deutschland ticket has increased to 58 euro.

And the trains are not very "scenic" due to tree, etc between the tracks and the river, but you can always get off and explore and then get on the next train.

the train you take could be cancelled or delayed

But with a train every hour, if your train is it ¾ hr late? Maybe it's ¼ hr early.