Carefree with

呑気(のんき) describes someone relaxed and free from worry. Depending on the context, it can criticize them for being too carefree or unconcerned.

Dictionary Definition

性格や気分がのんびりとしていること。こせこせしないこと。

One's character and mood are in a relaxed manner. Not being anxious.

Goo Dictionary

Examples

Careless until graduation with 呑気

Learn the meaning and usage of the vocabulary 呑気 in Japanese, with examples from manga.
アオハライド » Volume 13 » Page 18

Aya has mostly given up hope of attracting Shuko’s interest away from their teacher, Mr. Tanaka. Tanaka, having no interest in pursuing a relationship with a student, pushes for Aya to keep trying before the situation changes.

田中(たなか):
呑気(のんき)にしてるとあっという()卒業(そつぎょう)だぞ」
“If you act carelessly, it'll be graduation before you know it.”

No time to leisurely eat with 呑気

Learn the meaning and usage of the vocabulary 呑気 in Japanese, with examples from manga.
美少女戦士セーラームーン » Volume 8 » Page 58

After an enemy attack changes Usagi and Mamoru into kids, Usagi wakes to find the two of them living together as a couple. As Usagi wanders into the dining room, Mamoru is placing a plate of french toast on the table. He greets her and asks Usagi what type of jam she wants on her toast. Usagi responds, then realizes she needs to get to school.

うさぎ:
「あたし ライムのマーマレードッ」
“I'll have lime marmalade!”
「ってそんな呑気(のんき)()べてるヒマなんかあたしにはっっ」
“Ah, I don't have any time to be leisurely eating!”