You cannot buy pets using the recharged function or via donation but you can buy Colorful Shell to get taming items in-game.
Colorful Shell can be obtained also in Pet Quest in Pet Adventure Guide.

Colorful Shell cost 1 BIG CAT COINS per 10 Colorful Shell’s in the recharged function.

All you need to do is to click the Colorful Shell and it will open another option for the conversion or how much it cost for the certain taming item.

For the common pet’s, it will only 10 Colorful Shell’s for 1 Taming item, However, while the pet is getting rare, the amount of Colorful Shell is also increasing.

Though not all taming items are obtainable via Colorful Shell, like for example the Silver Knife of Chastity to tame Sohee, At least you will have a good start by just using the common one.
Please try to check the following article to know more about Ragnarok Pets.
Pet Labor
Pet Adventure Guide