With a tank for a group anchor, and DPS being a dime a dozen, I would roll up a cleric. Not only is it thematic, but you two will never lack those main pillars in forming up a party.
Any thoughts as to which race you will be playing?
If healing makes your eyes glaze over, an enchanter is looking to be the shizz.
I totally agree with Thunderleg that Healer or Support class would be the best choices. I have an additional suggestion.
Paladins have several bonuses when fighting undead. Halflings have a damage bonus against Wraiths. If you choose a Halfling class you can get some good syncronicity with a Paladin against Wraiths. Which there are many of in the Halfling zone, and likely plenty more around the world.
If you like Cleric or Enchanter, either will do just fine. If neither attracts you, then consider Druid as a healer or Bard for support. (Bard will be in the game, is just not guaranteed by release but likely). Either of these could be a Halfling.
In EQ, one of the best duos for Paladin was the Enchanter. Paladin with resource regen, haste, and slowed NPC from ENC was a force, while the ENC could also safely have a charmed pet with the Paladin's instant snap agro or nearly instant stuns/roots and quick heals to help out the ENC if a charm or mez unexpectedly broke.
As others have said, healer/tank combo is a pretty safe bet, but if like EQ, I fear it would get painfuly boring in a duo situation. PAL/ENC duo would have no problem finding a healer for grouping and would likely have a lot more fun as a pure duo team; Not to mention that they likely would not "need" a healer to accomplish quite a lot. Of course I'm comparing these to the EQ equivalent, in which case, all healers could do was buff and heal really (with the exception of a SHM slowing)... Cleric/Tank duo in EQ was BORING as hell. ENC was brilliant at CC/melee Buffs and supreme DPS via charm while PAL was master of staying alive or keeping others (particularly ENCs) alive in a pinch.
Some people may argue that the SHM slows on an NPC made them the best duo to go with a melee, but honsetly, the SHM slow basically made the NPC not deal damage, in which case a melee DPS (like a monk) paired way better with the SHM than a tank. I expect Paladin dmg to be 'one of' the lowest in the game.
My summarized opinion: (Using EQ as a comparison) I would personally steer clear of any melee or Tank class if you plan on playing duo with a Paladin, if one of you is playing a Tank or Healer, the other should play a class that is capable of soloing some content if you want to be succesful at duo'ing later in the game at all. The classes most capable of soloing will likely be the INT based casters, with the ENC (or possibly NEC) having the most synergy with a melee.