Frankly I think all colours should get counterspells. Apparently WotC are pretty down on counterspells generally because their market research finds them to be "un-fun", but they're a pretty key part of the game, especially in EDH for example (there are some threats where you basically counter it or lose)... and anyway, so long as they keep printing blue counterspells at all they should probably print some other colours IMO. Every colour has access to (forms of) removal, card draw, etc, so why should counterspells be colour-restricted?
White especially feels like a colour where you can make counterspells quite thematic, and it being secondary in them would be a way to broaden its slice of the pie and help with its traditional issues (in EDH at least). Imagine something like
Ashiok's Erasure in White - for example "1WW - Intercesion -
Flash. When ~ enters the battlefield,
exile target spell. When ~ leaves the battlefield, return it to its owner's hand. At the beginning of your upkeep, sacrifice ~ and draw a card".
Red got
Tibalt's Trickery not long ago, so that's one design, or it could be like an
Arcane Denial where you get impulsive draw, or something where someone can take damage to have their spell not countered. Black could be sac, discard or lose life or be countered, or have discard as well, or you sac as an additional cost (a way of making it a bit more restricted than just an unconditional
counterspell). Green feels like the least likely to have counterspells and that's no big problem IMO but, say, tapping a creature as part of the cost (indeed, a creature with greater P or T than CMC sounds sensible) would be interesting - Green typically wants to play big creatures at sorcery speed, and attack with them, so holding up the mana and the creature for that would actually be pretty significant.