In last 3 weeks, I talked to 3 girls who all seemed very positive in my approach, happily punched their digits and typed up their names in my cellphone. Usually I send a witty text the same night depending on the info I gathered from them during approach and they reply too. This also helps me give them my no. I don't reply after that unless their text requires me to.

Then after 2-3 days of gap I ask them for an innocent coffee in the evening 24 hrs in advance. Either I get no response or girl flaking out last moment saying she has stuff to do.

My questions are-
is a 2 min conversation and then couple of texts enough for a girl to agree to get coffee with you?
When is the right time to ask for coffee after you get the number?
Should I be texting more to build a rapport before asking her for a meetup?

No. You are still nobody to her. Ask her before you get the number. If you can, have coffee right there and then. No. Build rapport on the initial meeting. Use the phone number with the purpose to set up another meeting.

Read a lot of the posts on this site and you'll find out that guys often talk/text themselves out of a meetup before it happens.

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1. When you get her number, tell her that you are going to meet her for coffee. It reduces flakes. You can even ask like this "We should meet up for coffee, give me your number and we'll set up a time.". That way nothing is weird later on, and it makes her feel like she already actually agreed to meet up for coffee if she gave the number, so it's rude to flake later on, although if you didn't build report it's still very possible to get flakes.

2. Quick. If I had a really good interaction with a girl, I don't mess around afterwards. If I got her number super quick because she was on the go or something, then I might try to chat over text a bit but even then I'll only wait a few days. It's just coffee. If I message a girl "hey I'm free Sunday morning, lets grab a coffee" and she texts back "we don't really know each other that well" or anything even resembling that (anything that indicates that she thinks that meeting up for coffee is a bit fast or forward) I'll reply with "It's just coffee, I'm not gonna get on my knee and propose. I figured it would be a good time to meet up, since I stay pretty busy. So let me know if you're up for it."

Its a no bullshit response. If there's any attraction at all, meeting up for coffee shouldn't be a big deal. And you should let her know that you have high standards and that you aren't the kinda guy that's gonna be her phone buddy for weeks on end just to try to earn a coffee date with her. Guide her with confidence, and if she's attracted to you then it shouldn't be a problem.

3. Try to build plenty of report when you get her number because no texting game in the world makes up for making a good impression in person.

Some of my tricks to build report if I'm just grabbing a number.
- I'll send her a text right then and there, so she has my name. And it will usually be a funny comment or something like that. So when you text her later on she knows who it is.

- If we meet at a club, a party, a bar, or anything fun, as in the kind of place where you will be taking pictures, after I grab the number I'll tell her to put my number in her phone, then I'll hug her in and get her friend or get her to take a selfie of us. It makes you appear like a couple, and it's a picture of you two having fun. Then I grab her phone and set it as my contact picture. So every time I text her or call her, she gets a photo that reminds her of the fun we were having last time we met. If there's a really good connection I'll tell her to kiss my cheek for the photo or I'll kiss hers. Anything to show that I'm interested and confident.

I agree. You can very easily build more than enough rapport in the 2 minute timeframe you are talking about, you can have the girl wet and hanging by her phone for you to text her, and VERY eager to meet up with you ON YOUR TERMS, BUT you NEED to give her info about yourself during this time so you aren't just some random dude.

You have to form a very close connection with the girl by standing close to her, through your vocal tonality, through kino, through being VERY VERY comfortable with her and behaving with her as though she is your girlfriend in a classy way. If you approach with a friends vibe or with a gamey vibe, 2 minutes or 30 minutes is not going to have the girl wanting to meetup.

Reasons against long initial approaches: You can approach a handful of more girls in that time, it's somewhat of a DLV to have nothing at all better going on during the day than to chat with an "unproven" girl for a half hour, you could say ONE THING to ruin your shot with this girl ; they are on a mission to weed out guys so this is very easy to have happen.

With a shorter approach that contains the points listed earlier in this post, the girl can become VERY curious about you. You've got things to do, you're a busy man about the world, you don't have time to linger, on to the next thing, but make your connections with these girls count for something. Don't think of it as a game, think of it as forming real connections.

This works way better if you tell the girl what you want to do with her. Ask what she has planned for a certain day, then if she says nothing, tell her about some awesome plans you have (you can just make up plans if you actually don't have any). Then tell her you would invite her, if you weren’t convinced that she’s just using you for your body.

haha

She will laugh and then you can play off that for a while using the “I’m not just a piece of meat” frame.

Then TELL HER what you guys are going to do.

Say something like, “Alright we’re going to go to the mall. I’m going to make you my personal shopping consultant. You’re going to pick out some clothes I don’t like, I’m going to pick out some clothes you don’t like, then we’ll get into a big argument and ill end up locking you in a dressing room cause.....well.... I’m sneaky like that. Then we’ll make up and go get ice cream. Then we’ll go eat it by the ocean and watch the sun set as we talk about our passions.”

Make her picture the date with you in her head. It will make her want to go with you that much more.

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Thanks for all the good suggestions guys. I am learning new things here.
enlightenmentdating, I tried this on one of the girls that asked for a raincheck for a coffee date few days ago. Last Saturday I described to her the evening of xmas tree lighting and skating in nearby mall and she responded well, showed up, and we had fun. She agreed for a 2nd date too.