There is no way to buy crown store items outside of the game.
Which is unfortunate, for exactly this reason. They did have the option to buy items (the Imperial Edition upgrade and the Palomino Horse) directly through the website before the crown store was introduced, so it definitely is possible, and I would have thought it'd make sense for ZOS to ensure as many people as possible can buy their items.
I keep hoping they'll bring the option back, but it hasn't happened so far.
(BTW the one alternative is to give someone you really trust your login details and ask them to buy it for you. But I don't recommend doing that unless it's someone like your husband/wife, a parent...someone who has far more to lose by screwing you over than they can gain from it. Oh and they also need access to a PC with ESO installed.)
PC EU player | She/her/hers | PAWS (Positively Against Wrip-off Stuff) - Say No to Crown Crates!
"Remember in this game we call life that no one said it's fair"