The only pokemon i can think of really, is Tentacruel. Not weak to grass, but weak to electric. These specific weaknesses you mentioned only apply to either pokemon already said, or pokemon in ubers.
Anyways, 80 Special attack and 100 Base speed is fairly good. A Choice Specs set could work, considering Tentacruels bulkiness. It can cover a rain team easily, if used as a wall or more offensive support, it is wonderful. While holding Black Sludge and having its dream world ability, Rain Dish, it gets alot of HP back at the end of the turn.
Anyways, Tentacruel can set up Toxic Spikes and sit back, and lay in the rain and relax. It will wear away at any pokemon switching in, that is common on a rain team. Because of its natural special bulk, and the nature of water and ice moves being 9/10 special, Tentacruel can pull rain team countering off with aplomb. The only real counter is a Kabutops, Or Dugtrio. Dugtrio can trap you in and earthquake you and it will hit hard. Kabutops can tear through Tentacruel with a +2 Stone Edge. Anyways, I hope i helped to the best that i could. Now a summary, and set.
Since it isnt from the list, can cover and counter a rain team, takes neutral damage from grass, and has enough special bulk to take electric hits, i think this pokemon will suit you well. here is a set i would reccomend:
Tentacruel (M) @ Black Sludge
Rain Dish Ability
252 HP Evs 128 Special Attack Evs 128 Special Defence
Hope this helps!