You're correct; it is the zeros that are causing the options to be filtered. We normally have Logarithm, Box-Cox, and Arcsin, but all three methods are not defined for negative values or zeros.
If you are looking at transformations in preparation for kriging, we support Normal Score Transformations with simple kriging, and several of these transformations are applicable for negative/zero data values. Normal score transformations are performed within the Geostatistical Wizard.
EDIT: I misspoke. Arcsin is defined for data between 0 and 1 (inclusive). So it can work with zero values, but if any data values are negative or greater than 1, the option will be filtered. Because the option is filtered for you, you must have some data values larger than 1.