One can enforce non-default-initialization and non-integral initialization with

 struct onlydouble {
   onlydouble() = delete;                // OK, but redundant
   onlydouble(std::intmax_t) = delete;
   onlydouble(double);
 };

This enforces "non-integral initialization" only in the sense of causing an ambiguity in overload resolution in most cases, rather than through the "honeypot" behavior of deleted functions. This is also a poor way to enforce non-integral initialization, since the same ambiguity also blocks initialization with long double.