If you do not have a food processor, you can still enjoy home made mayo - with a lot of whisking and a bit of heat (Alex' s recipe will work easier, if your eggs and oil are at room temperature to start with).
Mix the ingredients (see Alex's recipe) and put in a pan of simmering water (in the same way you would melt chocolate) mixing all the time, keep going until you get the thickness you want and chill.