If your deviled eggs filling come out too runny, try adding a little instant mashed potatoes straight from the package. It doesn't affect the taste, and it firms them up nicely.
I just want to post that this works! It saved my deviled eggs! So grateful as these are for a church coffee hour on Easter that I promised to bring food to. I wasn't sure what to do as it was so runny it wouldn't stay in the egg white cups. It took about 1/2 cup of the instant mashed potatoes to thicken my runny filling that was for 20 eggs. I am not sure why it came out so runny, but might be due to using pickle relish without draining it as well as too much mayo. Anyhow, the mashed potatoes worked immediately and it looks and tastes terrific. The texture is perfect now!
It occurred to me afterwards that it probably would have worked to add baby cereal like the rice or the mixed grains and it would probably have thickened it without too much taste change. Didn't try that, though, but mentioning it in case anyone else comes to the site and doesn't have the instant potatoes on hand, but may have baby cereal. Good luck!
I thought I had ruined the deviled eggs I'm taking to Easter brunch tomorrow. Thought I'd have to run to the market to get and boil more eggs, but oh ye of little faith.....mashed potato flakes to the rescue!