No, they’ve never been romantic, and I don’t think sexual tension has ever even been hinted at between them. Which is kind of nice, really.
Natasha and Frank have teamed up on a few occasions: Punisher/Black Widow: Spinning Doomsday’s Web, Marvel Knights v2, and that Nathan Edmondson crossover maybe if you squint. But they’re antagonistic just as often: Rucka’s Punisher/War Zone, and most recently Secret Empire.
Edmondson, who wrote them both, summarized their relationship like this:
Their motivations and internal dialogue and moral codes are very different, though they both are on similar paths, though they wouldn’t admit it. They both might travel from point a to point b, too, but how they make that journey is very different. Black Widow sees Punisher as someone unfocused, uncontrolled, and purposeless; but Punisher would see Black Widow as an emotionally-driven “corporate gal” in a sense. They don’t have time or use or patience for one another, really.