It's a god, not a genie; his limit is $1.98, not $1.97; and it's the god who figures out how to make the man happy for only $1.98. The story is "$1.98" by Arthur Porges, also the answer to the old question Hero rescues a minor deity, granted a wish of small value; gets a [SPOILER]. It was first published in The Magazine of Fantasy and Science Fiction, May 1954, available at the Internet Archive.
"You mentioned a—a reward," he said diffidently.
"I certainly did," the god answered him, swinging on a dandelion stem and kicking minute bare feet luxuriously. "But, alas, only a small one. I am, as you see, a very small god."
"Oh," Will said, rather crestfallen. Then brightening:L "May I suggest that a small fortune—?" Truly the presence of an immortal was sharpening his wits.
"Of course. But it would have to be exceedingly small. I couldn't go above $1.98."
"Is that all?" Will's voice was heavy with disappointment.
"I'm afraid it is. We minor gods are always pinched for funds. Perhaps a different sort of gift—"