Daniel Prince wrote:

I have a handcart with tubeless tires. One of the tires has developed a
leak in the sidewall. It goes completely flat in about a day. (I wish
they had used a solid rubber tire.)

What is the best way to repair this tire? Would one of those liquid
tire sealants work? Thank you in advance for all replies.

You could repair it the correct way if you plan on keeping the tire.
Patch and / or plug the hole. You'll probably be able to find the cold
vulcanizing materials at your local auto parts store. You could also
take the assembly to the local truck tire repair folks ( industrial )
and have them foam filled. (Similar to a previous post.) Then they
will last forever ( almost, at least until the tread wears off.)