The '48 Parliament was hopelessly naive and terminally accommodationist. That's not to say the revolution couldn't have succeeded, but it would have had to go differently. The King of Prussia is the wrong horse to bet on, though. Even if he were to accept the crown, he would simply walk over parliament and create his own state in the medium term.
That's possible, but the Reichstag (which is what I'd propose the Frankfurt Parliament would become once the Second Reich comes into existence) would probably give the Prussian King a good deal of power as Emperor, and the Frankfurt Parliament is going to be important if the new Emperor wants to create a unitary state (which I would say this new Emperor does, since he accepted the offer to become Emperor). Basically, by accepting the crown from Frankfurt, the Prussian King has given Frankfurt a good deal of legitimacy and quite a bit of military backing. He's also made it likely that as German princes fall, the people who overthrow them will ask Frankfurt to annex them.
Throw in a foreign intervention, where Frankfurt enacts legislation to start levee en masse, and the creation of a large, albeit Prussian commanded, new German Army, and I think Frankfurt has shown its a useful body to have around. Frankfurt's also going to be writing the new German constitution. It might end up being curtailed or having less power, but I think that if the Prussian King accepts Frankfurt's crown, then he has basically guaranteed Frankfurt's continued existance.
I'd say your best bet is Western/Southwestern Germany. Support for a liberal solution is strongest there, many of the princes would be amenable, and it's right next door to France, whose support will be needed in the coming war. Of course, whatever Germany results will be the mother of all kleindeutsche Lösungen, but the chances are better for a nationalist reform of the Bund with Prussia and Austria leaving than it is for Prussia turning democratic.
I think Prussia was picked in large part because of its military. The Prussian King has the Army to make his Imperial reign stick. The small princes in SW Germany might be liberals, but they don't have the military force. Also, I would bet France is not going to support the creation of a united Germany. In fact, if some kind of united Germany emerged from 1848, I would bet that France might become part of international coalition to end the experiment in German nationalism.
The alternative would be a much more radical Berlin revolution. The majority of the Prussian population was fairly indifferent to their junkers, so if the good people of Berlin, instead of sitting down to talk and convince their king, had broken out the guilloutine early and started on the royal family and general staff, they could have taken power. Of course that is massively out of character.
And after executing these people, the other Army commanders who aren't in the city mobilize the Army, enter the city, and execute lots of people Commune of Paris '71 style. Then another branch of the Prussian royal family is found and placed on the throne. Berlin is a mess. The Revolution is over.
Frankfurt in '48 is the KEY.