In the manga, in some chapters we have demonstrations of something more solid than a simple friendship.
Let's get started:
In the Cap 30, when Barry the Chopper atacks Riza and fall in love for her, Riza calls Mustang for a little help to interrogate Barry. When Mustang cames, he see Barry with his hands around Riza's waist. So he says: Watch out Ltn., my flames tonight will enter in the story.
In the Cap. 37 Roy and Riza talk like a couple in the phone, obviously it's just a "code" for the mission (Riza have a codename: Elizabeth) but in the Cap. 62 we can see Madm Christmas asking for Roy: Why u don't have a date with Elizabeth? and Roy says: I loose her for other guy. *she is the new pessoal secretary of Fuhrer*. (other spoiler: Madm Christmas is the adoptive mom of Roy, but they always speak into codes in her meetings, like in this, Elizabeth = Riza)
In the Cap. 37 too, when Riza is atacked for Gluttony, Roy can hear and enter in a desesperate state, he gt into a car and says: I must have time. (to save her!)
In the Cap 38, after he save her and Fuery, she scream: U can't get in danger for us! (this is a resume) and after he says: I'm happy u are alive, ltnt. And she says: Thanks for this, Coronel.
In the Cap 39, when Lust says about Mustand death, and says that was she the assassin, Riza came in a crazy state, where she shoots at Lust even her amunnition ends.
After, she stop to shot and begs to Lust kill her too. Alphonse don't leave Riza, and minutes after, Mustang appears. Riza try run to him, bt Alphonse safes her.
After Lust death, Roy falls and Riza run to help him. So he says: U ar good, first lieutnt?
And she says: I even worry about it!
(And finally helps Mustang). He says again: Alphonse, thanks for protect my subordinate.
In Cap. 47, when Hawkeye and Mustang are alone in the "cottage" of Fuery, helping Al and Ed with the radio station, she have to get out to help Ling and the boys, she says: I'll enter in contact if I get some news, stay here.
So he says: Ok.
She says: It's better u don't shows your face there.
(angry face) So he says again: Ok, I get it.
(with the face "Calm, I never disobey you again)
In Cap 49, when Riza try to find and protect Mustang between the Gluttony's attack, he scream: Stay away! (With this, he saves she for a "walk into Gluttony's stomach").
After, when he was running out of Gluttony and the monster will swallow Roy, Riza appears and shoot in Gluttony, distracting him and saving Mustang.
She helps Roy to go to the car, bcause his injuries hurts, they are almost embrace. (In the japanese culture this is like a kiss or something like that).
In cap 56 shows Mustang worry about the state of Riza and he thinking that she isn't a idiot to wait for him for so long time. (one night and some hours waiting for him) But for his surprise, she appears, so she says: U are good? I was so worried about you.
So he says: U don't fled?
And she says: U says for me never run away.
In Caps 58 and 59 shows the beginning of the relashionship and shows that Riza's father was Mustang's master. Shows a lot of Ishvalian War too and a little of their relashionship at it.
In caps 60/61 we have more of their past. Ishvalian War and Riza's father burial.
In cap 72, Riza is at home, thinking in their meeting with Pride, when Roy calls. He realize a strange thing in her and ask: Wht happened?
She says: Nothing.
He: Are u sure?
She: Nothing. Really, but thanks for call me, especially now.
(I just say the important parts of the call) After the call she hugs Hayate and says: Why he have the gift to call in the right moments?
So the manga shows Mustang, the phone in hands with that face "She don't convinced me
Well, we have so extras too, and some official images too, but this is just the manga parts. (I don't know if I get all of the parts, but are the most of them here)
And Yeah, could be really nice if they stay together in the end. (Please Hiromu, make this for us!)