Can coyotes get into wire cages to get to rabbits, if so, how can i prevent it from happening.

Height. Put the cage high up, on stilts, for instance. No chicken wire, but a strong wire. Dogs around.

No, coyotes can not get into a wire cage (assuming it is properly made).  However the rabbits might get scared to death and just seeing the coyotes attempts to penetrate and without being able to run away) so better put the cage in a place beyond the reach of the coyotes and preferably in a protected place (e.g: Fenced area).

Coyotes can get into nearly anything.  If they see your rabbits, they will chew through chicken wire to get to them.  The best move is to put up a 2X2 wire fence around your rabbit hutches, make your hutches strong enough to resist 300 pounds of bite force, put on a strong roof, plenty of ventilation, plenty of feed and plenty of water for the rabbits.  Keep a cardboard surface for the rabbits to walk on until they have to defecate or urinate.  They will go there . . . most of the time.

The trick is to know how coyotes think: they are starving paranoids and they trust their sense of smell more than anything else.  If you keep the scent constantly changing, that will make the coyotes so nervous about your place they will think twice about going near it, until hunger drives them to go for your rabbits.

The old trick of keeping a bag of cat food someplace distant from your rabbits doesn't work.  As soon as they polish off the food, they will be hungry again and think your rabbits look very tasty.

One thing helps, though.  Empty your cat box upwind of your hutches now and then.  A few days later, sprinkle some strong smelling detergent somewhere else near your hutches.  After that, deer scent from the hunter pro shop (that tells the coyotes that hunters are there and they are in danger.)

Go out to feed your rabbits twice a day at no certain schedule, and once in awhile pee on the ground to maintain a strong human smell.

Either that or put your hutches inside.