"作打油诗的人" can be translated into English as "a person who writes doggerel" or more simply "a doggerel writer".
"Doggerel" refers to humorous, often nonsensical, and usually rhythmically irregular poetry, which aligns with the characteristics of "打油诗" (dǎyóushī) in Chinese.
"A person who writes doggerel" directly describes someone engaged in this activity.
"A doggerel writer" is a more concise way to refer to such a person.