Don't coo at a dog who is nervous, but you can reassure him with calm, confident, ordinary talking. Show him by example that you are not worried. If you allow yourself to become worried because of his anxiety, you'll be confirming his suspicion that there is something to worry about.
Ideally this is an elevator you can divert for desensitization training for five minutes several times a day. If so arrange to hold the elevator on your floor while you do the exercises and don't allow it to move at least until he is confident in it when it is still. Exercises include:
- Going in, getting a delicious (high value) treat, and then coming back out again without going to another floor.
- Going in, letting the door close, getting a delicious treat, and then opening the door and coming back out again without going to another floor.
- Eating all meals inside the elevator, without going to another floor. This is the part that will hold the elevator up for 5-15 minutes.
- Going in and playing with a toy with your dog for a minute or two, then back out with no ride.
Try to assess what specifically about the elevator it is that makes him uncomfortable. If you think it is primarily the texture of the floor (slippery) or that the floor moves, then choose a bath mat with a rubber backing to be his elevator "magic carpet." If you think it is the vibration, or a combination of the vibration and floor texture, then choose a piece of 4" thick high density furniture foam (available at craft stores by the yard), or just rip the cover off an old sofa cushion and cut to size.
Spend time in your home teaching your dog to lie on his personal magic carpet. Make it the most wonderful place in the world to be. Feed him his meals on the carpet. Give him treats every time he lies on the carpet. Ask him to lie on it and load him with praise and attention when he does. Good things happen when he is on that carpet. You can grab a spray bottle of DAP (dog appeasing pheromones) and spritz the magic carpet with that or just cover it with a dirty tee-shirt that smells like you.
When he's okay going into the elevator and coming back out and he thinks his magic carpet is super fantastic, then it's time to combine the two exercises for a ride. Up until this point, I'd try to carry him down the stairs, even if the thinks the stairs are worse. Any unpleasant experiences with the elevator will undo counter conditioning progress until he's ready for this part.
Now during the ride you can praise the snot out of him and give him loads of positive attention for lying on his magic carpet. He's already used to that. Being on the carpet is good and it's something you've consistently highly approved of in the past. So lay it on thick and say whatever word you've given to the carpet over and over so he knows that's what you're making the fuss about. "Look at Joey on his carpet! He's such a clever boy and it's such a wonderful carpet." And so on.
Later you can wean him off of the carpet, but for a while it's going to be his security blanket. The nifty thing is that because it is portable you'll be able to use it for more than elevator rides. You can use it for anything he finds stressful, such as a trip to the vet or a car ride. Get him over the initial hump and then gradually wean him off so that he builds confidence in himself and trust in you even when the carpet is not present. Remember to always keep that carpet charged with loads of good things like dinner, treats and loads of affection at home so he can carry those positive associations with him when he needs to go someplace stressful.