All of these are from a work entitled Enshō nazo tsukushi ("Naughty puzzles selection"). I presume the book is of Edo vintage based on the art style, lettering, etc. but can't precisely date it because my edition is a modern facsimile with absolutely no publication information at all.

"Someone who just can't get enough, no matter how many times they do it."

"A loose woman -- or an old person visiting the ceremony!"

(Didn't Carnac the Magnificent do this one?)

"Something that gets dug right away."

"A flighty woman's latest crush -- or the earth where a horse just took a leak!"

(Because it's good for fertilizer, I guess? Also, pardon my reliance on the hippie usage of "dig". The original uses the word horeru, which can mean either "fall in love" or "get dug up".)

"Something that dribbles juice as soon as you split it open."

"A ripe watermelon!"

(You can't really say this in English without sounding mildly psychopathic. I just wanted to point out that although the standard format is to give both halves of the double-entendre in the answer, thus making it two single-entendres, this one doesn't dare clarify its saucier implication. Conclusion: there were limits.)

"Someone who gets lucky underwater."

"A fisherman -- or Urashima Tarō!"

(I'll admit it: I laughed.)