Well you won't like the first answer, kick them in the groin, get their mind off the technique, shin is really good if you know how to kick. But here is some principles and concepts that can be applied.
First of all the lock you do to them and their response, only exists at that time in that place. So try changing the angle that you apply it to. We use the 'clock' system, 12 at the head, 6 at the feet, and so on around the clock. We also use it on the floor, so you can step to a certain angle. 12 being in front of you 6 behind. Aikido does this on an octagon system(happundo) and many systems talk about the 45' angle. So try applying and stepping to different angles. Try going into a stance, not just the "T stance, but long or cat or horse stance. By going into a stance it will drop your weight, and shift your weight. You can do this in T-stance as well. Shift you weight, drop your weight, move to a different angle, apply to a different angle, all these might help. Hakko Ryu Jujutsu uses what they call a mitsubushi, which is a back flick to the eyes, this will cause the person to move back and then try the lock. we call this 'changing prioriotes' or change their mind set, get them thinking somewhere else. I think if you to to the trouble to mistubushi, you might as well hit them, so we strike before we lock, to get their mind off what I am trying to do. When I do these locks on friends or relatives, I always step hard on their foot, then take the lock, and show them how to transfer the pain. Its a cute way of getting it done, without really hurting them. You can also apply the lock to their center, or yours and this will change the locks dynamic.
As for Nikkyo, I will offer a version that we use. We use the concept of Fulcrum-Lever- Base from Professor Wally Jay's small circle Jujutsu. In this variation, we use both hands on the hand, the principle of push/pull is also used. Your pinkies should be in the crease of the wrist, this is your fulcrum. We use our thumbs on the thumb knuckle,our thumbs and pinkies are matched up with each other, our thumbs push(lever), the pinkies pull(fulcrum) and then we go into all the ideas given before, apply to their center, or yours(base), change the angle with the hand, change the angle with your feet, go into a stance. A final thought is do the Nikkyo like your doing a downward block to your center(change the base), this version changes the position of the hand, and always have success. However, we ususally start things off with an 'inner gate kick' or shin kick to start things off before we lock. If a punch is thrown, we "tenderize" them before applying the lock.
Our version of Ikkyo is quite different, and its not very Aiki, so I won't share that, but try to use different body parts on the elbow, such as your forearm, elbow or even hammerfist the elbow. I use a wrist bone strike to tricep and that usually works as well.Once again try changing angle, and weight distribution during the technique
Trying to explain a technique over the internet is tricky, especially not knowing how you are doing it and if you are technically on with the lock to begin with. I usually will not show technique on family members for 2 reasons.
1. If I take it easy and it doesn't work, they don't think the technique is good, or that I am.
2. If I do it hard, or the way it's to be applied, they get mad because it hurts and they think you broke their arm.
These techniques are meant to apply constraint, and in some cases pain, its the pain compliance in some technique that makes it work. You can hold someone down with Ikkyo without causing pain, but then again without it they may squirm around. Nikkyo without pain is Nothing so you need the pain to get that lock to work. If you try to take off the pain compliance, the lock won't work, so by going easy with a friend etc...you won't get your lock. you need to apply pain if its going to work. People are usually hesistant to inflict pain, once they have experienced the pain of say Nikkyo, especially to family or loved ones. I always, always apply pain to any lock, no matter who asks. So...if you want to see the lock, I will show it but warn you, its going to hurt. If you are going to apply it, you need to APPLY IT as you would for real, but with control. This should help things out. Remeber, if you want it to work, you got to apply it, no matter who it is.