Having done quite a lot of relaxation therapy for more serious reasons than success at croquet I would strongly endorse what David [above] said here - essentially he is also talking about cognitive behavioural therapy, based on avoiding negative thoughts and looking for the rational reaction to any bad stuff that happens.
The technique it is very simple. The basic technique is to using breathing to relax. When you breathe out it invokes a natural relaxation reaction - that is why we sigh at moments of great stress or when something stressful is over. You can do the relaxation in a single breath when on the lawn and for shooting you need to focus on relaxing your shoulders. First you need to practise the relaxation technique and learn to focus it on a particular part of your body
Do the practice sitting or lying comfortably. Take a deep breath in and hold it, clench your fists, curl your toes up, compress you stomach, lift your chest as high as possible "stiffen the sinews" every muscle in your body arms shoulders neck buttocks legs. Then breathe out with a deep sigh allowing every muscle to relax. Observe the feeling of relaxation in your muscles so that you can recognise it easily. Repeat several times until you are sure.
Now repeat the deep breath (in Yoga it is called a complete breath) hold it for 4 again and this time breathe out counting down from 8. On each count focus on a different part of your body:- 8 - right arm, 7 - left arm, 6 - right leg, 5 - left leg, 4 abdomen, 3 chest 2 spine, 1 head. As you focus on each part of your body feel for the relaxation reaction that you learnt in b) and focus on getting that part of your body to relax
Now repeat but using one complete breath for each of the 8 body parts. As you relax each body part imagine that a hot sun is shining on that part of your body making it feel warm and relaxed.
You should now be completely physically relaxed. Focus on your breathing. Breath normally only as much as feels natural. As you breathe in through your nose say the sound "Saaaaahhhhh" to yourself, as you breathe out through your mouth say the sound "Haaaaahhhhh" It should sound like waves breaking gently on a sandy beach. On every hah breath send the warmth and energy of your breath to any part of your body that needs to relax more.
When you can do that you just need to do the deep breath, as David said, before you play your stroke, together with the mentally positive thoughts "I am going to hit this!" and, as David said, banishing absolutely any negative thought.
This works for me.
I also think that a good warming up routine before a game is worthwhile - I use some simple Yoga exercises concentrating particularly on those that work on the back and shoulders. I think that Tai Chi warm ups are also good. Certainly the basic Tai Chi stance is right for hitting in.