Most economical Transportation from Nuremberg to Munich airport

Flixbus goes from Nuremburg directly to the airport for as low as 7 euros, but only at 06:00 and 09:00
https://global.flixbus.com/

The train goes to the main train station in Munich where you then would transfer all on one ticket to the SBahn

I think there are direct buses, but if the timing works, you can go with a Bayern Ticket, 39 EUR total for 3 people (13 EUR pp). The Bayern Ticket includes use of the Nuremberg U-Bahn and Munich S-bahn. Fastest way departs Nuremberg Hbf on the 6:08 Regional Express to Munich Hbf, then change to the S-1 to the airport, getting you there by 8:46. Be aware there is a 10 minute transfer time from Track 25 on the main level to the underground S-Bahn station. If you miss that one, take the S-8 going the opposite direction and it will get to the airport at 8:55.

Apart from the two Flixbusses mentioned above, there are no bus connections between Nürnberg and MUC. And even three weeks out the Flixbus fare is €19.99 pp. So it's better to travel by train on a Bayern ticket per suggestion of Sam.

What time is your flight? What time do you need to check in?

We are going down to Munich the day before our flight.

You can use the Bayern ticket to travel to Munich for 39 EUR for 3, and use it for the rest of the day on the Munich transit system. There are many regional trains running between Nuremberg and Munich, but some can be very slow, making a lot of stops. Regional Express trains that go a few minutes past 6 am, 9 am, 11 am, 1 pm, 3 pm, 5 pm all take 1 hour and 45 minutes and are the quickest.

To get to the airport, the nominal single ticket cost is 11.60 EUR pp, but you can buy a group all-zone day ticket for 24.30 EUR so you'd pay 8.10 EUR pp to get to the airport. S-1 and S-8 trains go in opposite directions through the center of Munich, but both end at the airport. Each train goes every 20 minutes and alternate so a train arrives at the airport ever 10 minutes.