I have been looking to see if it's possible to program Arduino boards without the use of a computer. Just wondered if anyone has tried that or if it is just not feasible
MCU vendors do offer off-line programmers.
STC and Nuvoton are two examples, and these typically have Serial Flash that is loaded with your binary, and then a PGM button can update MCUs without
needing PC connections.
Field use and production line programming are common uses.
If your code is only small (uses < 75% of the ardunio), you could use any ardunio to copy a block of its own memory to a programming port.
If you want to pgm 100% of code area, you will need some external flash/eprom/etc memory to copy from.