Here are a couple I've used and had good luck with. The first uses a stick blender and the second a bar blender.
Stick Blender Mayo
1 egg at room temperature *
1 1/2 tablespoons lime juice
1/2 teaspoon salt
1 teaspoon dry mustard
1 cup salad oil
Crack egg into wide, straight-sided glass jar (mayo?). Add remaining ingredients. With the motor OFF put stick blender down to bottom of jar. Then turn it on and, rocking it gently from side to side, pull it up to the top in about 8-10 seconds.
******************************
Mayonnaise
2 egg yolks *
2 tablespoons mustard
Dash salt and pepper
Squirt of lemon juice
1 to 1 1/2 cups oil
Put ingredients in blender, and blend slowly, adding oil until you have desired consistency.
Yield: 1.5 cups
*RAW EGG WARNING
Suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.