To add to the answer above, (and this is kind of a world building answer), but your scenario, at the very least, would be unusual and difficult but maybe not impossible. The answer is a little surprising, but the way to do it is to make the moons smaller and bring them in closer to the planet. They'd have less gravitational interaction with each other that way.
It's not difficult to have a moon with a 60 day orbital period. Our moon, for example has a 27.3 day period (sidereal) with an apparent 29.5 day synodic cycle, full moon to full moon, but the moon basically circles the sky in a little bit over 24 hours because of the Earth's rotation. Any relatively distant moon will orbit it's planet slowly.
But that's not really the issue. If the planet has normal days, similar to 24 hour days on Earth, and I'm guessing by your question that you don't want the day/night period on your planet to be huge, then any distant moon's apparent orbital period will be determined by the planet's rotation period, similar to our moon which appears to orbit the Earth about once a day (25 hours or so). If your planet has what we might consider regular days, 12 hours, 16 hours, 24 hours, what have you, then your 9 moons would need to crowd around the geostationary radius and crowding an orbit with 9 objects that would be visible from the planet's surface is never a good idea.
9 visible moons from the surface along is a lot. Jupiter has over 60 known moons and more waiting to be discovered, but most of those wouldn't be distinguishable as moons from the planet's surface. Only the big 4 would be clearly identifiable as moons. The rest are too small. 9 visible moons is a huge number and crowding those 9 moons around the geostationary orbital radius is nuts.
But there is a way to do it and it's straight forward math. Bring the geostationary orbit closer to the planet by making the planet less massive and by increasing it's rotation period, shortening it's days.
Take Earth as a starting point. Earth's geostationary orbit is about 35,786 km above the equator, and the equator's radius is 6,378 km, so for orbital purposes, it's 42,164 km from Earth's center of mass. Both numbers are relevant.
If you reduce the mass of your planet to 1/2 the mass of the Earth (orbital period formula is proportional to (r^3/m)^.5), r^3 needs to equal 1/2, so r is reduced to 79.3%.
And if you increase the rate of rotation of your planet from 24 hours to 16 hours. The period is now 2/3rds and, same formula, the ratio of the period to the radius the power of 3/2. 2/3rds the period equates to a 76.3% of the initial radius. Combined, with these factors, the new geostationary radius, from the center of mass is 60.6% of 41,164, or about 24,933 km from the planet's center, or about (assuming 5,100 km radius for the smaller planet). 19,833 km from the surface.
If you make the planet even smaller or the planet's rotation period even faster, you can bring the moons even closer. So, why does this help you?
As you bring the moons closer to the planet's surface you can make them smaller and they can still be visible. As you make a moon smaller, say you reduce it's radius by 50%. It's mass is reduced by a factor of 8 but it's angular diameter is only reduced by a factor of 2 and it's apparent brightness by a factor of 4. By shrinking your planet and by increasing it's rate of rotation you move the geostationary orbital radius closer in and you can make the moons smaller but they can still be visible. By making them smaller, they would have less gravitational interaction with each other and you could theoretically have 9 small moons in tight orbits, visible from the planet's surface, with relatively long rotation periods. You could explain the collection of small moons as the result of a collision between two moons. It's a stretch, but not impossible.
If you want astronomical accuracy though, moons that close to a planet would pass through the planet's shadow fairly often and given their size, they'd probably disappear from view. You could offset that somewhat by giving the planet a sizable axial tilt and the moons orbit the planet's equator, but they could still pass through the planet's shadow as the planet approached it's spring and fall equinox.
All that said, most of the Moons should still have a not that slow orbit, 1-2-3 days. Getting a 60 day orbit requires the moon be very near to the geostationary radius and another with 15 days, that's also quite close. You shouldn't have to many moons with long period orbits because there's no realistic way to do it, but you could have 2 maybe 3 in the 10-60 day range, and I'd push the others out into the 1-2-3-5 day range. You could even have a retrograde moon if you wanted. It wouldn't really be retrograde, it would just appear that way because it orbits the planet faster than the planet rotates.
If you wanted to get creative, you could have a Janus/Epimetheus dance. :-)
A final point. Your moons in this scenario shouldn't be round. They would be small enough to be lumpy potato like objects.