Vowel is to diphthong as consonant is to?

The directly analogous term is indeed consonant cluster, a combination of consonant sounds that appear together.

It is possible that you are thinking of a digraph, which is two characters representing a single sound, rather than a blending of adjacent sounds as with a diphthong or consonant cluster. For example, the ch in church or the sh in hashish are digraphs.

The technical term is simply "consonant cluster" or "consonant blend". As spoken, they are part of the general class of "phonemes" (especially "digraphs", groups that indicate a non-transitive mouth position, such as "th").

Many phonetic alphabets have specific characters for phonemes that we use consonant clusters for; for instance, the Greek "theta" is a single character that Romanizes to "th". Norse runic lanuages had the "thorn" character, with much the same purpose. The Russian character ш is pronounced similarly to "sh" as in "show". By contrast, the Japanese alphabet is made up primarily of consonant-vowel pairs, and the only "consonant clusters" seen in Romanized spellings involve "n", which is the only consonant sound that exists unpaired in gana/kana (it also exists paired).