I've flown several times with my child at the ages you mentioned. If you're nursing, you'll probably be fine with the 2 month old. And most likely that child will sleep for a portion of the trip. But remember, you're 21 month old might want your attention, so you'll have to trade the kids around most likely.
As far as the 21 month old - if it's not too much of a pain, I would bring his car seat with you as well. First, ask if the flight is full. If it is, check the seat. If not, bring it onboard (even though you did not pay for an extra seat). I am not sure what airline you're flying, but if it's open seating, then you could secure the seat right next to you. I have done this several times, and the stewardesses have no problem (as long as the flight is NOT full). This was wonderful because it freed up a lap and he actually fell asleep in his own car seat. (Which, brings me to the point of bringing your own seat, as opposed to renting one when you get to your destination.) Your child will be more comfortable in his own seat. If he normally catches a nap in that seat, he will continue to do so. If it's new, he may be too interested in how different it is and that will keep him awake when traveling.
To help "carry" the seat around the airport, I hooked ours to the back of our stroller by connecting the tether straps together. Basically I put the seat facing me (while pushing the stroller) and connected the tether straps together over the handles. (kinda confusing, but try it out).
Now as far as entertainment on the flight - when reading online, people recommended buying a couple "new" toys. I went to the $1 store and found some cheap cars, squishy balls, etc. that really kept my child's interest. I also packed snacks that took a while to eat (goldfish, cheerios) and some favorite snacks like gummies (shaped like cars and tractors). I rarely give lolipops, but had some on hand just in case. (You may want to pack a bib for those.) In addition to this, I brought some old and new books that seemed to help.
Coloring books and stickers are an idea too, but I found they didn't keep my child interested as long as I hoped!
As a gift I received a Color Wonder book and marker that is awesome! It's 1 marker that turns the page all different colors when the marker hits it. It's awesome because you only have to worry about 1 marker and it will not work on anything other than Color Wonder paper, so you don't have to worry about it getting on anything. If you're child likes to color, this is the way to go!
Best wishes!