Muriel is a good support, you just don't build her as one as her entire kit is her support items she doesn't need more of it she has Movement Speed Buffs, Attack Speed Buffs, Shielding and an ult designed to save your allies from certain death if you are going to play her as support you have to build her for damage.
Consort Crest > Tranquility | Gives you a heal that you can use once you shield your allies after going in with your ult it grants a 400 HP heal with 10% damage mitigation not to mention 20 haste making this an essential item on Muriel if you plan to go damage on her which I think is the best way to play her as it rewards hyper aggressiveness and map presence.
Oathkeeper | Right off the bat this item gives her 60 Magic damage poke this isn't much until you build the rest of your kit, but it is useful to have as it grant you steady damage as you level.
Lifebinder | The Purpose of this item is team fights as it buff your abilities further, granting you some snowball potential and a decent amount of healing.
Prophecy | Muriel has the highest damage Magical Autos in the game clocking out at 200 damage and since this build will take advantage of haste this item becomes a very useful item by allowing her to help out in wave clears and fights.
Combustion | With her High Attack Speed and Decent Magical damage this item becomes a no-brainer as she will be able to proc it with regularity allowing her to melt a team with ease and letting your team get some easy kills.
Oblivion Crown | All of Muriel's Skill have a buff passive on them that scale off of her Magical Power the more she has, the better her Buffs are, I have been able to give my carry 70%+ Attack Speed with 100 Magic damage to his auto attacks nearly indefinitely due to its 3s cooldown. Not only that but in combination with Combustion this item can do a third of an enemy's health in damage, securing kills for you or your carry.
Magic Tonic | Duh.