The latest client (0.6.2) contains the new CLI command:
test (unlocked) >>> help wallet_account_historic_balance
wallet_account_historic_balance <time> [account_name] Lists wallet's balance at the given time
Lists wallet's balance at the given time
time (timestamp, required): the date and time for which the balance will be computed
account_name (string, optional, defaults to ""): the name of the account for which the historic balance will be returned, "" for all accounts
test (unlocked) >>> wallet_account_historic_balance "2015-02-26T23:20:00"
test 95.09268 BTS
test (unlocked) >>>
The double quotes around the timestamp are mandatory. The timestamp must be given in GMT.
Please note that the balance calculation relies on the transaction history, which is known to be buggy - so double check the results for plausibility.