Though there really is no actual dictionary word that rhymes with orange, there are other ways that Orange can be rhymes.

Compound Words

This ways to rhyme probably makes the most sense. Compound words are two words combine together, like door hinge, that is used to rhyme as one word. 

Orange Rhyme by Michael Gregorovich

There once was this girl Angeline,

Who knew how all things should have been.

When they said “Get the door, Ang”,She said “It is orange but should have been painted pine green”

Proper Nouns

There are some proper nouns that comes close to rhyming with orange, like this US Naval Commander named Henry Honychurch Gorringe, or Blorenge, a hill in Wales

Local Note by Arthur Guiterman

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In Sparkill buried lies that man of mark,

Who brought the Obelisk to Central Park,

Redoubtable Commander H.H. Gorringe,

Whose name supplies the long-sought rhyme for “orange.”

Enjambments

Enjambments are one or two syllables of a word sometimes added to another word to rhyme, which is very confusing at times to read, and even harder to read out loud fluently.

The Unrhymable Word: Orange by Willard Espy

The four eng-

ineers

Wore orange

brassieres.

But even with these, there isn’t a single word that can satisfy the rhyme for orange, and that should be telling you something: The person who invented the word needs to get his eyes checked