"Somebody asked me to be their sponsor, but I'm not sure I want to. They never get to a meeting on time -usually they come in half-way through. They talk for twenty minutes, or talk 2 or 3 times. They never talk on topic. They're always in a crisis. They're not very good friends with another person I sponsor, and there's a lot of drama going on there. Is it okay to say no when someone asks me to sponsor them?"
Yes, absolutely. I wouldn't sponsor someone who won't come to a meeting before it's half over.
I'm not going to speculate about what that may or may not indicate about the person who's always late, because this isn't the place and I don't think it matters - the motives behind the actions may be completely obscure to the person themselves. Dealing with only the result of the choices, the following is happening:
The meeting, and whoever may be speaking when this late person arrives, is interrupted. They avoid sitting in silence, listening to the readings common to the opening of an Al-Anon meeting - the greeting, Preamble to the Steps, the Steps, Traditions, 3 Obstacles to Success.
They "hijack the meeting" by ignoring the topic and speaking instead of the (most recent) crisis in their lives. They talk for so long that they leave little or no time for the other people who might like an opportunity to share.
An AA friend would describe behavior of this sort as: "There's a lot of "me-me-me!" going on.."
I think most of us could be described as self-absorbed when we come into program, because we're so caught up in our own problems that they "fill the screen." Even that being so, most people are still able to detach for the sake of politeness and offer courtesy and some space to other people in a social setting. If someone won't do this even in an Al-Anon meeting, which is grounded on giving each person room and space - well, I said I wouldn't go there, so I won't. Suffice it to say that if asked to sponsor someone who is always coming into meetings half an hour late, I might reply that I would be happy to do so, after they'd shown me that they could be on time to a meeting, and once there, respectful to the other members, for a period of 3 months.
I consider sponsorship to require a serious committment of time and energy on my part, and after this many years doing it, I have a good idea of my own limitations. I know that I don't want to work with someone who is disrespectful of both program, and the other members of the group. I don't want to embark upon a caretaking relationship thinly disguised as sponsor-sponsee. I can't make someone want to change. I can't love someone into wanting to change. I don't want to work with someone who is more interested in acquiring another spectator for the drama of their lives, than in working their program - I've made all these mistakes in sponsorship, and learned the difficult lessons therein. Hope this helps.