Good luck! You'll be sooooo much happier.
I am not a doormat 
. Perversely, a somewhat abusive childhood led me to cure myself in early adulthood. I have some tips...
I have noticed that doormats over-explain themselves. This makes it harder to say "No". They tie themselves up in knots finding an "acceptable" explanation of why they can't bend over backwards. In the meantime they prevaricate, waffle, generally fail to say "No" even though they want to.
You don't need a "good reason" to say no. You might find it easier to stop feeling guilty if you stop explaining yourself (assuming you do over-explain).
It doesn't matter one jot why you are saying no. Normal people don't actually care why you are saying no, they are too busy thinking of different solutions to their problem. Users (not normal people) need to be told "no" very clearly so they know it is not open for "discussion", i.e. brow-beating you into submission. "No" without explanation is absolutely clear.
I learned to only explain if I genuinely want to help but circumstance is stopping me and I want the friend to feel comfortable asking in future.
Examples from last few years where request was identical.
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Pregnant friend asked me to pick up her kid from school when she was puking her guts up with morning sickness but I had a dentist appointment for a cracked tooth. I said no, explained that I couldn't because of dentist, and that it would be OK to ask in future if necessary, I'd be happy to help. She did ask again. I did help. We are friends.
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Massively disorganised friend asked me to pick up her kid from school again when she was running late again. I work longer hours than her ffs with younger DC. Last two times she asked I just said "Oh, no, I can't do that today, sorry" in a neutral tone of voice. I had no reason other than mild pissed-offedness, I gave no reason even when she huffed and puffed and sounded a bit peeved. She found other solutions. We are still friends.
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Friend asked me to pick up her kid from school. I was feeling exhausted that day. Crap reason to not do it really but I know my limits. I said "Oh, no, I can't do that today, sorry" in a neutral tone of voice. I did not give a reason. She found someone else to do it. She wasn't bothered. She's nice, she doesn't want her friends to feel put-upon, she's OK hearing no. We are still friends.
Remember, you don't have to find/offer an alternative solution when you say no. The other person is an intelligent human being who can find their own solution.
If, like many a doormat, you find it hard to stop talking after "Oh, no, I can't do that today", "oh dear, no, that won't work for me", remember people love talking about themselves. Ask them a question about themselves or their situation.
You could say sympathetically "Are you having a bit of a mare today?", "How's Burt's lumbago?", "Oh poor you, car still not fixed, how annoying for you!".
You've already said "No", so you both know you aren't engaged in a negotiation, you are just being a nice person offering a shoulder to cry on (which is a hugely valuable characteristic in a friend).
If the person tries to pressure you, STILL DO NOT EXPLAIN and disengage from conversation asap, "No, really, I can't today. I'm in a bit of a rush myself at the moment. Good luck it sorting out. See you later. Bye".
Slights, put-downs, little disrespects (a favourite of my toxic mother and her family), raise an eyebrow or give a little incredulous giggle, "Saucer of milk with that comment?!", "Got out of bed the wrong side today, did we?", "Yeah, yeah, if you say so ", "Thanks for that. Very helpful ".
I find it helps to recognise that disrespectful behaviour is a sign of the other person's personality, especially tendency to bully. It actually has nothing to do with the reality of you. React accordingly.
Surprisingly, I learnt the above from my DF who is a bully. He is exceptionally good at dealing with bullies himself. I can put him back in his box easily these days. Wow.
If putter-downer persists or escalates, raise eyebrows, say "Well, this is lovely but I really must be off now, see you later" and walk away / put phone down / talk to someone else. It's the only way they learn.
One of my brothers has definite people-pleaser doormat tendencies that he fights to keep under control. He says it helps him to remember that you help no-one by enabling a bully to bully. You can only help them by setting clear boundaries and enforcing them, in the nicest possible way, probably while saying sorry, of course 
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Flipping heck, that's almost a book!
Good luck!