Instead of 'want to get coffee?', mention you'll be near them and let them invite you, or offer what you actually want to give.
The idea
Every request for someone's time puts a burden on them. "Want to get coffee?" obligates a reply, and if they're slammed, it makes them feel like a jerk for saying no. Most people don't feel good saying no. Relationships run on how we feel about each other, so before you ask, think about the feeling you want to deliver. Maya Angelou said people never forget how you made them feel.
How to do it
Ask yourself what you actually want, then match it:
You have knowledge, a skill or an opportunity that would help them? Say so directly and offer to explain it.
You enjoy spending time with them? Ask to meet, but give them an out. Mention you'll be nearby and let them invite you if they're interested and free.
You want to show you care? That's usually the real one. It rarely needs courtside tickets or half a day at lunch. A text saying you're thinking of them often does it.
Example
When someone invites me to coffee, the socially awkward 12-year-old inside me gets super excited. Then the responsible adult with two kids, multiple businesses, a heavily medicated dog and a Peloton streak gets frustrated, because now I also have to be the jerk who says no. And of everything I've taught, the simple thinking-of-you text has produced the most incredible results.
Script
Instead of "Want to meet for coffee?": "I'll be in Dupont Circle on Friday and thought of you - is your office still there?"
Five Alternatives to Coffee: Instead of coffee: take a walk, go to their favorite spot, cowork, attend a talk together, or discuss one question in a small group.