There's a bitcoin escrow service called ClearCoin that includes the option of sending escrowed funds to one of their listed nonprofits, rather than back to the payer, if the escrow expires. I asked the site owner to include the SI donation address as an option and have been using it since.
Unfortunately for SI, everyone I've dealt with has been honest so far! I'll have to actually donate on purpose instead of incidentally, it seems.
Update: 14.01 bitcoins are "in the mail" (read: sitting in ClearCoin waiting for the transaction to expire). At current exchange rates, that's around $100.
Now you can donate to Singularity Institute using Bitcoin.
Currently Bitcoin mining appears to be profitable as only bubble economics can be. Already some Less Wrong users have purchased GPUs and started mining Bitcoin. Please consider sending some Bitcoins to SI at address 1HUrNJfVFwQkbuMXwiPxSQcpyr3ktn1wc9
2014 Edit: Please donate Bitcoin by using the Bitpay link on MIRI's donate page. Thanks!