I am usually very honest with friends and they are with me- we don't text each other things like 'are you free?' because that's quite rude, and implies the person will definitely want to see you if they are free!
I'd say the truth, I've got a half day but I'm not sure what I'm up to yet, and leave it to her to ask what she wants.
I couldn't be arsed with all this, in my world it's fine to be tired, move something to a better day or to do something spontaneous if the other person wants to, and none of this has to be achieved by telling white lies or any other types of lies, I know my friends want to see me, but they also don't take the piss and ask for favours for no reason either, I completely don't get any of these types of friendships!
If she said can you take my child, I'd say no, it's my half day and I want to chill out when mine aren't around, but I could do a playdate next week at X time. Or if she wants you to run her to the tip, she can ask that.
The onus isn't on you to make up excuses, its for her to explain her vague request which is obviously cheeky or she would just ask it straight out- coffee, favour, childcare and then let you judge.