1. Amendments are easier to pass than it may seem at first. The first requirement is a 2/3 majority in both houses of Congress. That happens all the time. Just look at the margins by which the PATRIOT Act was passed: All but a small handful of votes in the lower house, and all but one in the Senate. And that's not unusual at all. The next requirement is the approval of the legislatures of 3/4 of the states. That's not difficult either. The (informally) proposed flag-burning amendment was brought before Congress by petitions from 49 state legislatures (including Massachusetts!). The only restraint on rampant amendments to the Constitution is that it's still considered somewhat taboo to tamper with our most basic document. Every time an amendment is proposed for the redress of a specific grievance, that taboo is eroded further, and the results can be unpredictable and catastrophic.
2. A constitutional amendment, far from rebuking activist judges, will actually encourage them further. By amending the Constitution, we're tacitly admitting (however much we protest to the contrary) that they had the correct interpretation of the Constitution prior to the amendment. By default, it will give them carte-blanche to do whatever else isn't specifically prohibited by special amendment. Their attitude will be that if we don't like their ruling, we can always amend the Constitution. Even under a dangerously expedited process, we won't be able to amend it faster than they can pump out bad rulings.
As for alternative remedies to the situation, we have:
1. Impeachment. As others have pointed out already, this would be very difficult politically. But the more we concentrate our efforts to that end, the more attainable it will be.
2. Restriction of appellate power. Congress has this power over the federal judiciary, as part of its ordinary powers. It should definitely make use of it. The appellate power is the stick by which the federal judiciary pushes states around.
3. And finally, states should just ignore unconstitutional rulings from federal courts. If Georgia is told that it must grant marriage benefits to a same-sex couple who were "married" in Massachusetts, Georgia should say to the ordering court, "After careful mature study of your decision, we've arrived at the conclusion that it's not worth a pile of mule dung, but you're welcome to try to enforce it here anyway. Regards, ".