Instead of putting it all in macros you could write the algorithms once in a "template include file" array_template_impl.h:

    #define CONCAT2(a, b) a##b
    #define CONCAT(a, b) CONCAT2(a, b)
    #define ARRAY CONCAT(array_,ARRAY_ELEMENT_TYPE)
    #define ARRAY_FUNC(name) CONCAT(CONCAT(array_,ARRAY_ELEMENT_TYPE), CONCAT(_,name))

    typedef struct {
        size_t size;
        size_t capacity;
        ARRAY_ELEMENT_TYPE *data;
    } ARRAY;

    ARRAY *ARRAY_FUNC(create)(size_t size) {
        ARRAY *p = malloc(sizeof(ARRAY));
        p->size = size;
        p->capacity = size;
        if(size) {
            p->data = malloc(size * sizeof(ARRAY_ELEMENT_TYPE));
        } else {
            p->data = NULL;
        }
        return p;
    }

    //...

    #undef ARRAY
    #undef ARRAY_FUNC
    #undef ARRAY_ELEMENT_TYPE

Then you can use them with the #include code generation trick like this:

    #include <stdlib.h>

    #define ARRAY_ELEMENT_TYPE int
    #include "array_template_impl.h"

    #define ARRAY_ELEMENT_TYPE float
    #include "array_template_impl.h"

    int main() {
        array_int *ai = array_int_create(0);
        array_float *af = array_float_create(0);

        for(int i = 0; i < 10; ++i) {
            array_int_push_back(ai, i);
            array_float_push_back(af, i * 0.3f);
        }

        array_int_free(ai);
        array_float_free(af);
        return 0;
    }

(In practice you might want even more indirection files: Put #define and #include in array_int.c. and array_float.c, and create also array_int.h, array_float.h and array_template_decl.h with just the usual declarations.)