We've already redone the penny multiple times, the latest being in 1982 when the current copper-plated zinc composition was chosen. given the desire to maintain a visual difference with the dime, aluminum is not an option. That leaves either copper-plated steel (as is used in the Canadian penny at a cost of about 0.8¢ each) or a radical redesign. I can't see a radical redesign as being accepted by the public, so while we could probably eke out a few more years for the penny by switching to a steel core. Copper-plated aluminum would be cheaper, but is probably out of the question as copper-plated zinc has problems as it is with corrosion due to the difference in the electronegativity of the two materials and the difference is greater with copper and aluminum.
Well, as I said, stick a hole in the middle. That'll counter any change in material to maintain a different look. You might also be able to change the shape instead - make is square or better yet an octagon, though there might be some issues with machines that use coins with that. (not that too many of those use pennies nowadays) The treasury needs to stop thinking in such outmoded ways and figure out a good solution.
If you've reduced materials by 1/9, then you might not get a significant savings on each coin individually, but long term you would get a good chunk of change. Let's say we switched to steel cores and use the Canadian price of 0.8¢. Cutting out 1/9 of the material could make it about .71¢ per coin produced. The US government produces about 7 to 8 billion pennies every year. You would save a net $6.3 to $7.2 million annually. Sure, that's not much in terms of the federal government's budget, but it's still a significant amount when it comes down to it. If we use aluminum then we'll get less savings per penny, but it still over time it adds up.