punny

• (Received Pronunciation) IPA^(key): /ˈpʌni/, /ˈpʌnɪ/
• (General American) IPA^(key): /ˈpʌni/
• (Northern England) IPA^(key): /ˈpʊnɪ/
• Rhymes: -ʌni

From pun +‎ -y, possibly influenced by funny.

punny (comparative punnier, superlative punniest)

1. Involving the use of a pun.
2. (of a person) Fond of puns.
3. (of a pun) Funny. (Can we add an example for this sense?)

   Synonym: puntastic

• punster

Clipping of punishment +‎ -y

punny (plural punnies)

1. (school slang) A punishment.

• puny – small