Hauling personal furniture items to states.

Just for informational purposes, if I had a friend hauling a 16 foot or so enclosed cargo trailer here to take some of my personal household furniture items back to the states, crossed at Pharr or McAllen and left to return the next day and drove straight through, would it still be necessary to stop and obtain permits for the truck and trailer?  Also which day of the week would you suggest?  Don't want to do anything illegal but would like to make it as hassle free as possible.  Thanks for your input.

It is a little unclear but if your friend is coming from the US into Mexico to do this, he/she will need to obtain a tourist permit at the border, a TIP for the vehicle/trailer combination and Mexican auto insurance for the package.  Upon exit, the TIP is turned in and the TIP deposit refunded.  I have done this many times without any issues.  As long as all the TIP paperwork is valid for the vehicle/trailer combination that is being used, it is the correct way to do it.

Crossing at Pharr/McAllen is easy and no particular day of the week is any better or worse than any other from my experience. Saturday and Sunday mornings though are particularly quiet if that would work out.

I read the question as can your friend drive a truck and trailer in from the states and back out again the next day without stopping to get a TIP for it. If he does not want to do anything illegal, then no he can not do that. Even if he would not mind doing something illegal he might mind getting arrested and his truck and trailer confiscated along with your furniture if he actually made it here from the border without displaying a TIP on his windshield.

I knew driving 30 plus miles into Mexico required a TIP but wasn't sure if I could get some type of permit for a short-term haul. When I do this I'll just pay the TIP deposit by CC and tell them I'll be back in a day or so and they can refund the deposit to my CC.

No special haul permits. Transporters for pay are supposed to be licensed and are regulated for interstate transport. Your driver would have to claim the trailer contents as his personal property, etc,, etc.
You did not mention the origin of the truck/trailer, which is important since a commercial sized foreign truck would be denied. A Mexican truck hauling goods to the USA would be suspicious, I would think, making it likely to be detained at the US border.

No, a 12 foot or maybe a little larger enclosed plain cargo trailer like my 5x8 I brought down here. I would be with him and I have my MX driver's license and residente card. I would fly to the states, meet him, drive down with the empty trailer and then return with my three or four pieces of furniture. Nothing new, all antique. Just don't have room for everything in my trailer.

Then, Yes, the truck and trailer will need to be temporarily imported and the deposit paid. The driver and occupant must complete the required immigration documents in and out. All perfectly normal. When the truck/trailer exit Mexico together, the deposit will be refunded to the same credit card used to post it on entry, or in cash if cash was used on entry.