Hi Gerard, here's my attempt.
I think you guessed correctly - you cannot use potential and passive together because the form is the same. I think that normally to say "can be ...ed" we convert the passive into normal form. Or keep the passive as it is, and add such phrase as "...kotoganai", "...hazuganai", "kesshite...nai" in place of potential.
He
cannot be defeated.
kare wa uchimakasarerukotoganai.
This code
can be understood if you have the appropriate key.
kono angou wa kaidoku dekiru
They
cannot be persuaded.
karera wo settoku surukotohadekinai.
Phone calls
can be traced.
tsuuwa wa gyakutanchi(surukotoga) dekiru
One expression I can think of is "... kanouna". But I don't think it is equivqlent to "-able" as you can use it only in certain cases - you can use it only when you can covert the verb into noun. (...siuru is another way)
Otherwise you have to use clause, not one word; "....(surukotoga)dekiru"
or use the verb as modifier. Sometimes ...beki.
breakable: hakaikanouna, kowasukotogadekiru, kowaseru
drinkable: nomukogotadekiru, nomeru
likeable: koukannomoteru
foldable: oritatamikanouna, oritatamukotogadekiru, oritatameru
readable: yomeru, yomigotaenoaru
Yes, ... tewaikenai is correct. More formal expression is "....tewanaranai".
Tewanaranai is mostly used in writing while tewaikenai can be used both in writing and daily conversation.