I assume you may want more or less instant access to this money, so pension payments or other investments aren't appropriate here...(?)
If you have a family member or significant other in whose name you can open an account, open two Rabodirect accounts with €10K in each. Because they only pay their headline rate of 4.75% on amounts up to €10K. Leave those accounts sit.
Stick the other 10K into a Northern Rock account (where it will earn 4.3% gross) and (again, if possible) open two regular saver accounts with Halifax. Or even three, as you and your partner can also hold a joint a/c in addition to one in each of your own names. Then set up DDs for the same date to the Halifax accounts from whatever account your regular €750 saving was going to come from — presumably the account into which your salary is paid? Let's call this your 'transit' account.
Once a month, 4-5 working days before the DDs to Halifax are due, log on to your NR a/c and transfer an extra €1500 into your 'transit' account (that's presuming you have three DDs for €750 going out to the three Halifax accounts).
That's about the 'lowest-maintenance' way of doing it I can see!