Yes, Bookly supports deposit payments. To be able to use deposits you'll need the Deposit Payments (Add-on), which can be found here.
Help Center
https://support.booking-wp-plugin.com/hc/en-us/categories/200390561-FAQ
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FAQ
Questions about Bookly products and settings
custom
https://support.booking-wp-plugin.com/hc/en-us/sections/200751971-Getting-Started
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Getting started
Instructions related to plugin installation and usage
community
/hc/en-us/community/topics
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Community
Join discussions with other users
new_request
/hc/en-us/requests/new
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Submit a request
Contact us through a specially prepared form
installation, shortcodes, appearance