White Putits (just called Putits in game) are level 1. You should be able to
A. Dominate them using the Domination spell OR Rods of Domination at any level, especially with the precious item Monster Heart, which is itself obtained from the quest "Mia's Dream". This adds the putit straight to your party, and it will probably be minced if you don't protect it immediately. On the other hand, this means you won't risk losing it as an inventory item, and can simply keep it dead until you can scrounge up enough gold for a Deed of Ranch. Which are expensive.
B. Catch them with a leveled Monster Ball. To use a monster ball, you have to weaken the creature. The problem with this is that putits are so weak you will have trouble not over-killing them, unless you are ALSO level 1. There are several places to obtain monster balls, including a quest which gives you six Lvl 5 balls. The quest asks you to return five of the balls with a monster in it, so you can keep one for yourself-Just don't have it in your inventory when you give the old man his! Using a monster ball (press Shift-T, throw it at the weakened putit) will fill the monster ball, allowing you to carry the putit around-just be warned that you can drop it on death, and filled monster balls all seem to weigh ten stones in my experience.
There is something I will add.
Red Putits are slightly stronger (only slightly), so they may be easier to safely weaken, and are not as easily minced by enemies. I think they might give more CHA. Because of their slightly higher level, though, they will breed slightly slower. You see, breed power goes down as level goes up-though the upshot is that the bred creatures are sometimes stronger.
You might also try for the military putit. Compared to the Level 1 Slime Tourist (White) Putit and Level 3 Slime Red Putit, the Military Putit is a Level 6 Slime Gunner. They are also neutral, rather than hostile, so you don't have to fight it immediately. They come with their own guns, usually, and may give you trouble if you don't let other weak enemies damage it, but they have this silly little hat, and a microphone on their side. They may actually be usable companions in combat. My biggest concern, however, is figuring whether or not they still raise CHA when eaten.
I doubt the level 12 Putit tank is even edible, so I won't go over it.