Hierarchical deterministic wallets (HD wallets, BIP 32): https://github.com/bitcoin/bips/blob/master/bip-0032.mediawi...
Stealth addresses: http://sx.dyne.org/stealth.html
The former is more broadly supported.
You could also just log in and supervise two automated systems interacting, rather than entering numbers.
(Mind you, I don't believe in the glorious future of bitcoin, but any wider usage will certainly be accompanied by better UX)