A portable AC will. You may even find that maybe 2 portable units do a better job where you actually spend your time and may actually reduce your cooling bills since your central AC never shuts off. Many various varieties of casement windows (no matter side or top open) you can also just remove the entire pane without much effort and make a plywood slug to go in its place to hold the AC. Given the choice, a window unit will work better.
Still, with only a 10-12 degree delta I'm thinking something may just be "wrong", as CM is saying. My old house was like yours and I discovered it was because the "renovators" I bought it from had 100% blocked off the return air ducts by literally capping them off with plywood and dry walling over them. The only thing I could do was open the return air up in the basement and make sure to leave the basement door open at all times. It helped, but obviously wasn't ideal.
The long-term fix to that would have involved me building a plenum where the duct USED to be where a pantry USED to stand. Glad I sold the house before I bothered with that nightmare...
If you get a portable AC unit, YOU MUST get a two hose model like this one.
If you dont run a 2 hose system, you're screwing yourself. With a 1 hose system, its drawing conditioned air out of the house to blow that air across the hot side of the system. So more air is being drawn in from the outside making the unit work harder.
In a 2 hose system, it draws hot air from outside, runs it across the hot coil, and dumps the waste heat back outside where it belongs. Conditioned air is drawn across the cool side. No new air is pulled into the building.
Ive used these repeatedly and they work well. Far better than the cheap units my folks have bought locally from big box stores. Those last a season or two running 24/7 (supplemental cooling in a server closet). Knock on wood, these units have lasted many seasons.
https://www.amazon.com/gp/product/B0028AYQDC/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1