While any decent quality tuner will work for you. You may find that the strings stay in tune a bit better with classic guitar tuners since they have a larger diameter roller section that may grip the nylon strings a bit better. Either way, you won't lose.
If you get regular tuners you can try 'tying' them in. Start your string as usual. Then bend it down and allow the rest of the raps to go over the top of the string. Exaggerated in graphic below. I've ben doing this with electric guitar strings ever sense I learned to change them.
Hi Michael, tuners made for nylon strings are best but that would mean a slotted peghead. Steel string tuners work ok, but make sure you have enough post above the surface to accommodate the thicker strings.