Unlike in English, where you can combine random letters of the alphabet to form nonsensical words to mimic a sound, sound effect words in Chinese are all borrowed from existing characters, sometimes adding the 口 radical to indicate it is a sound, e.g. 口 + 瓜 = 呱, we can only choose the character similarly pronounced like the sound effect the most.
Frogs make more than one kind of sound, 'ribbit' is just one of them. "呱呱" pronouns as "gua gua" is similar enough to a kind of sound frogs make
To mimic the sound of 'ribbit' we have only one character in Mandarin that is pronounced similar to "ri" (Rì), and no character is pronounced as "bit"
It is easier to match English sound effect with Cantonese because it has 9 tones instead of only four in Mandarin, 'Ribbit' would sound like 列別 /lit6 bit6/ in Cantonese
If you don't like 呱呱, you can use 咯咯, but you can't make up a new character for the frog sound