How many batteries can be safety connected (in Ah) to the charge port of CR310 and a 30W solar panel?
Any size 12V sealed lead acid battery is safe to connect.
There is a practical battery size limit due to the charging current limit. A good power supply design goal is to fully charge your battery within 3 sunny days. With the 1 amp charge current limit, it would not be advised to connect a big 100 AH battery. Depending on local conditions, it might take more than a month to charge that large battery.
Size your battery for the number of days reserve you need for cloudy days.
Size the charging system to fully recharge during the sunny days between storms.
This post is under review.