There are no "docile' tarantulas - only specimens within species that are more tolerant of being handled than others! Grammostola aureostriata, Eupalaestrus spp. and B. smithi are very tolerant of handling as are some of the other Brachypelma spp. and some Avicularia spp. especially, A. avicularia. Stay away from any theraphosid from the Old World regions i.e. Africa, India, Asia, etc. from taxa such as Haplopelma, Poecilotheria, Thrigmopoeus, Selenocosmia, Chilobrachys, Pterinochilus, Augacephalus, Stromatopelma, Hysterocrates, Phoneyusa, etc. And, New World tarantulas of the taxa Lasiodora, Ephebopus, Megaphobema, Pamphobeteus, Xenesthis, Nhandu, Acanthoscurria, etc.
Also, remember that not all specimens within a species will possess the same temperament. Grammostola rosea (the common rosehair tarantula) is commonly recommended as a 'good' beginner species, as is Aphonopelma seemanni. However, there exists a great variance in temperaments among specimens of both species and temperaments may change from one stadium to the next.
In my opinion, G. aureostriata, A. avicularia and B. smithi are three of the best "docile" tarantulas. Of all theraphosids, I'd go with A. avicularia as the most inoffensive and "docile" species.