I've run into a similar predicament with aCar, and couldn't find an absolutely optimal solution.
I configured aCar to export daily backups (aCar > More Options > Settings > Automatic Backup: Frequency), which get automatically created in /sdcard/zonewalker-acar. I then used
FolderSync to sync that folder to The Cloud (Drive, Dropbox, etc).
aCar doesn't automatically import the backups, but it was easy enough to go to aCar > More Options > Import/Export > Full Restore and point to the most recent file before adding any new records.
Like I said, not really ideal (at all) but it worked for me.
I'd highly recommend keeping a separate copy of your backup in a different folder until you get all the kinks worked out.
I know that aCar was recently purchased by
Fuelly, so I'm
hoping that the app will get some sort of built-in sync option before too long. In the meantime, though, this is (sadly) the best I could come up with.