First, don't pay attention to people complaining about you 'feeding' if it's normal games. Explain that you're still learning that champ or role, and get on with your life.
Second, as stupid as this sounds, playing passive can be a good thing. If the enemy isn't regularly trying to trade with you and winning, you're generally fine. If the enemy isn't bothering you, and you're doing a better job of getting CS than them, you're probably also fine.
Third, try playing Sona with an AP build instead of the low-ELO meta build for her (something like:
), and going with slightly less support focused runes (Summon Aery, Manaflow Band, Transcendence, Scorch, with Resolve secondary using Font of Life and Revitalize). Such a kit gives her some pretty scary damage on her Q (actually, at higher levels of play, she is just as much of a poke support as a healer), and will let you play somewhat more aggressively while still giving you decent support utility). If you can get the hang of playing her like that with a focus on making it a kill lane or keeping the enemy marksman away from farm, you'll probably find you have an easier time playing other champs and rolls more aggressively.
As far as ideas, here's some champs who might be worth trying without having to adapt too much:
- Malzahar mid: He has a rather passive-aggressive play-style, mostly sitting back while his summoned voidlings and his E tear people and minions to pieces.
- Ziggs mid or bot: Everything he has but his auto-attacks is AoE. This makes it very easy to poke people while getting CS. He also has a reasonably good escape with his Satchel Charge.
- Sivir bot: Her kit in general is very well suited to playing more passively and still harassing the enemy simply by farming. She's also reasonably easy to learn once you get the hang of the spell-shield, and can be played more aggressively.
- Zyra mid: Plants, you've probably dealt with them before, so I won't go too far into descriptions here.
- Heimerdinger pretty much anywhere: Drop a few turrets, and sit back while they chew through your enemies.