We have some handy-dandy definitions of "pastoral," from the Oxford English Dictionary Online, that totally apply to this novel:
3. a. A literary work portraying rural life or the life of shepherds, esp. in an idealized or romantic form. (Substitute Dawn's cows for sheep and we have a match.)
3. c. A rural and idyllic scene or picture. (This is probably strongest in the third part of the novel, when the Swede remembers his early life with Merry and Dawn in Rimrock.)
Often the pastoral is presented as a contrast between an idyllic, peaceful countryside, and a dangerous, chaotic city. In this case the dangerous, chaotic city is Newark, New Jersey, Roth's hometown. The collision of rural and urban is hammered home for the Swede when Merry bombs the Rimrock post office, killing a local doctor.
She's described as "The daughter who transports [the Swede] out of the longed for American pastoral and […] into the indigenous American berserk" (3.114). The word "indigenous" is important. It alludes to the indigenous or original inhabitants of America, the Native Americans, and the extreme violence done to them in the name of the American dream.
So, given what we know about the pastoral, what exactly is an American pastoral? Many readers and critics see the title phrase as meaning something like the nebulous American dream. The Swede achieves one popular version of the American dream—working hard, having a fancy house in the countryside, with plenty of money, and a "perfect" family. As a third generation immigrant, he has completed the dreams of upward mobility put into play by first and second generations. His religion is America. He loves everything about it.
Then his daughter Merry becomes aware of the Vietnam War and America's role in it. She comes to believe that people only get rich by making war (not love), taking advantage of others, and hurting others… especially the poor and the powerless. She comes to question her father's version of the American dream. She comes to think of it as false and exploitative.
So, is the title ironic? Does the story argue that that there can be no such thing as an idyllic life in America unless the problems of poverty and war are solved? Will America always be haunted by the violence done to the Native Americans and the institution of slavery? How about by violence done in wars? There are no easy answers to any of these questions.
In fact, American Pastoral seems to be all about asking really hard questions, stirring things up, asking us to question our realities and our assumptions about American life and the American dream.