Since there is no single native American language, there is no single word with the meaning "rabbit" or "coney" but many hundreds of different words in hundreds of languages.
Just a few examples are:
Natick..............................wautuchques, mohtuckques
Ojibwe.............................waabooz
Algonquin.........................wàbòz
Cree.................................wâpos
Naskapi............................waapus
Abenaki............................mateguas
Maliseet............................mahtoqehs
Mi'kmaq............................apli'kmuj
Mohegan...........................tuksáhs
Shawnee...........................pit-tic-kin-ne-thie
Delaware (Lenape)...........muschgingus
Cheyenne.........................vóhkóóhe
Arapaho............................nowootooku
Blackfoot............................ááattsishaa
Choctaw............................chukfi
Cherokee...........................tsisdu
Mohawk..............................kwa'yenha
Nahuatl (Aztec)...................tochtli
Sahaptin (Yakama).............. xuuplá; nukásh (snowshoe rabbit)
Sanish (Arikara)....................wáRUx
Lakota...................................mashtinchala
Navajo...................................gah
Yaqui......................................taabu
Hopi........................................taavo
Shoshone................................daa'bu
O'odham..................................tohbi
Zuni..........................................ok'shiko
Rabbit is a symbol of fear. It is commonly believed that one "calls" their fears to themselves, by speaking them aloud. Rabbit's lesson to mankind is to not allow your fear to hamper you in your everyday life. Some fear is a good thing or we would walk into danger too frequently and be hurt or killed, but we should not allow fear to keep us from getting on with our lives.
Please realise that not all Native American tribes have the same beliefs and interpretation of symbols, I have given you what I was taught.
A bear claw (usually a depiction of the bear's head is at the base of the claw on statues, idols, etc) is a symbol of strength and resiliance in Native American mythology.
"...the Manzanita tree, a symbol of rebirth and new beginnings, in the traditional Native American mythology." www.archimuse.com/publishing/ichim04/4763_Srinivasan.pdf
The Raven is considered in most Native American mythology as a trickster and a creating god. It is said that the Raven also helped the Norse god Oden to find out information on the world of both the living and the dead.
Bird
Native Americans speak in language not in symbols.
it was a native American good-luck symbol
A butterfly symbol means "Everlasting Life" in the Native American culture
The medical symbol stands for Hermes's speed in Greek Mythology.
In mythology Adonis is the symbol of male beauty. In Greek mythology, he is a handsome hunter and the god of beauty and desire. He represents rebirth and fertility.
According to Native American traditions, the wolf is the animal that represents generosity. The turkey is also thought to be a symbol of generosity.
The symbol for love in Najahe is a crescent shape with a bead hanging from below it. This symbol was used on horse bridles.
Daphne is the laurel tree. That is what she became, not a symbol.