Yes, there definitely are rides where one adult can take two children. I'm sure others will chime in with more specific rides, but here are ones I can think of off the top of my head:
Its a Small World: We could fit our family of four (two adults, two children) in one row in one of the boats, so for sure you could do an adult with two children in one row and the other adult with one child in another row
Casey Jr Circus Train: There are different sorts of cars on this little train that can handle different size groups--we like the "monkey cage" car and our family of four all fits in together. Last time we rode in it with a family of three.
Storybook Land Canal Boat: It's a boat, lots of people ride in it (multiple families at one time).
Astro Orbittor: My husband rode in one rocket ship with both of our children seated in front of him while I took pictures. The catch is that only the child seated at the front of the rocket ship can do the controls--the child in the middle position is just along for the ride.
Buzz Lightyear Astro Blasters: The seats are pretty big here and I think you could fit three in the seat, but there are just two blaster "guns".
Pooh: The seats are pretty wide--we split into groups of two and two, but I'm positive we could fit another child in our seat.
Big Thunder Mountain: My husband took both of our children on this ride and said it was fine with both of them sitting with him in the same row/seat. (I'm not sure exactly how it works--my back can't handle rides like that.)
Those are the ones that are coming to mind right off the bat. Hopefully others will give you specifics on other rides. I know I like to know details of things like this.