Pygmy date palm (Phoenix roebelenii) is a small palm reaching 6 to 9 feet in height--small and aesthetically pleasing for most home landscapes. If you prefer to grow a different palm with similar fronds and mature size, match the growing needs of the alternative palm with the conditions in your garden. For example, place a sun-loving, dry soil palm in a similar condition, and avoid putting shade-loving palms in full, hot sun.
A rare palm native to the coastal scrub of the Florida Keys and western Caribbean is the buccaneer palm (Pseudophoenix sargentii). It's sometimes called the cherry palm. Although it grows to a mature height of 25 feet, it is very slow growing and lends itself well to small tropical gardens and courtyards, much like the pygmy date palm. Buccaneer palm has gray-green pinnate, or feather-like fronds atop a singular, but attractive trunk with a swollen base, like a gray turnip. This species needs full sun, at least 6 to 8 hours of direct sun daily, and a well-draining soil. It should be grown in frost-free locations, such as USDA Hardiness Zones 10 and warmer. It also is highly tolerant of seaside conditions.
Native to the Mascarene Islands in the Indian Ocean, the bottle palm (Hyophorbe lagenicaulis) has few but large pinnate, feathery fronds atop a bottle-shaped trunk. It is slow-growing and tolerates seasonal drought and full sunshine. In fact, if ample water is provided in a well-draining soil in summer and then drier conditions in winter, the attractive bottle trunk shape is accentuated. Grow this palm in frost-free gardens, USDA Zones 10 and warmer, where it will slowly reach a height of 15 to 20 feet.
Also called dwarf sugar palm (Arenga engleri) is a clustered, multi-stemmed species that reaches a mature height of no more than 10 feet. It is native to moist subtropical forests of southern Japan and Taiwan, and as such tolerates both partial shade and full sun exposures if the well-draining soil remains moist. It is best in a partially shaded garden, where it receives shifting, dappled sun and shade across the day. It is tolerant of frost and mild, short bouts of subfreezing temperatures, appropriate in USDA Zones 9 and warmer. This palm suckers, or sends up little plants from its base, to form a mass--but they can be pruned away to keep the palm looking more narrow and tidy.
Several species in the botanical palm genus or group Chamedorea could substitute for a pygmy date palm in a more shaded garden setting. The cat palm (Chamaedorea cataracticum) forms a cluster of pinnate fronds. This palm matures to a height of 6 feet with cluster width of 6 to 10 feet with its arching fronds. Parlor palm (Chamaedorea elegans) is a single-trunked species with pinnate fronds that reaches a height of 6 to 9 feet. Both the cat and parlor palm must not succumb to freezing temps and are limited to USDA Zones 10 and warmer. However, a tall, clustering species, the hardy bamboo palm (Chamaedorea microspadix) reaches a mature height of 10 to 12 feet and is much more cold tolerant. Bamboo palm grows in USDA Zones 8 and warmer.
Cycads are not palms but ancient plants that are related to modern-day conifer evergreens. Their fronds are pinnate, feather-like, and look like palms. Very slow growing, cycads will eventually grow a trunk-like, stumpy stem with fern-like fronds on the top. However, increased propagation of cycads by nurseries may provide you options of large size to replace a pygmy date palm. Look for king sago (Cycas revoluta) or virgin palm (Dioon edule), which both are hardy to USDA Zones 8 and warmer.