Putting tubes in the tires, is a given, put slime tubes in the little trailer
If it has already popped off of the bead, get an inner tube shoved in there and be done with flats. It will fix ya right up.
Why? I've owned several garden tractors and two CUT's, and the only time I've ever put a tube in a tire was when a tire was damaged, and I didn't feel like replacing it.
I hate tubes in drive tires. Especially low-pressure tires like what's commonly on these little tractors. Tubes in non-drive tires are fine, although I will still stay tubeless unless all other options (short of replacing an $$ tire) have been exhausted. I will replace a $30 tire before I throw a tube in it. Some folks will put 4-5 $10, $15, $20 tubes in a $50 tire before they see the light. Worse yet is that they will pay somebody to do it.
Why the vendetta against tubes? Because they do nothing to improve the overall reliability of the Tire/Tube/Wheel system. Often the valve stem doesn't fit perfectly through the hole in the rim, creating a stress point on the tube, or allows dirt in via the hole that later wears through or punctures the tube. Moisture can also get through that imperfect seal and then that rusts the wheel, creating a lot more work to go back to tubeless or completely ruining the wheel for use with a tubeless tire. And just because you have the right size tube in the tire, with the right type and location of the valve stem, doesn't mean that it will STAY PUT in there once the tire is returned to service. Drive tires that are exposed to high torque loads, will often shift position on the rim. This can happen gradually or all at once, depending on the load applied. The tube will shift position with the tire, creating stress at the valve stem, tearing it, or worse, just pulling the whole ^&%^$ing stem back inside the wheel. Remember, these are not car tires inflated to 30+ psi (not that ANY reputable tire shop would put a tube in a car tire) and not bicycle tires inflated to crazy pressures with rims that require tubes to seal. These tires are typically inflated to 8-14 psi and it's pretty easy to shift one on the rim.
I do like slime tubes (or adding my own slime to tubes) for small tires like those on hand trucks, walk behind blowers, dump carts, wheelbarrows, etc. But that's about it. There ARE exceptions to my rule
like the guys that run corrosive tire ballast in larger tractors with big $$ rims. But those tubes are typically installed as such that they seal up pretty good. I'd prefer non-corrosive ballast but that's a whole 'nother thread.
My main gripe is that 90% of the time, tubes are installed to save a chitty tire that needs to be replaced regardless, or installed as a "go to" solution for minor conditions that are easily corrected, often without removing the tire from the rim, and then it's often installed incorrectly or in a tire that's used in applications that are inappropriate for a tube.
Tubes are for bicycles.