A solid champ pool means champs that you enjoy playing and that you can reliably pick. It sounds to me like you might just not be sticking with a given champ (or set of champs) long enough to get to the point where you love them and want to keep playing them. Just a guess, but it's possible.
- If you put Support as either your primary or secondary, then you'll reduce your chances of getting autofilled. If you're support primary, it'll pretty much never happen, so you'll always be able to play the same champs.
- If you go with popular or flavor of the month champs (say Yasuo or Jhin), your champs have a high likelihood to be banned or picked by the other team, and that lowers your likelihood of getting to play the same roster frequently.
- If your pool is too large, you won't be able to focus on learning to love the champs you're playing.
So if we combine those, here's one possible pool you could end up with.
Support primary: Sona + Leona. Both have fairly small pick/ban rates, but are common enough that ADCs will know how to play with you. And their roles are different enough that if your ADC asks for a support that can poke, or play defensive sustain, or super aggressive, or focus on peeling, you have someone that can get the job done.
Top secondary: Malphite + Nautilus. You won't be getting top often with support primary, so focus on only playing one. Just put in a couple games with the other one for the super rare cases where you're top and your normal top champ gets picked/banned. And tanks are pretty much always useful. To paraphrase Riot: "Amumu's win rate is high because Amumu's team always has at least 1 tank on it, making it statistically a better-than-average team composition."
Whatever pool you end up with, for it to be solid, you should only have 1-3 champs in 2 roles (plus a couple supports for auto-fill if support isn't one of your main roles). So come up with a small set of champs, and then just stick with them for a specified period of time. Maybe try a month? And if at the end of the month you end up really hating Sona or whoever, then you can try new champs. But force yourself to stick with the same champs for a while.