When someone is reluctant to give you referrals, it's likely that they're concerned about their friends' or colleagues' reactions to their names coming up in conversation and to your calling them.

They could be afraid that their friends or colleagues wouldn't appreciate having a salesperson unleashed on them.
This fear or concern isn't intellectual; it's emotional. Let your clients know you share their concern, then reframe their thinking. Here are two of the best reframing techniques for overcoming referral objections:
HOW YOU CONTACTED THEM
Remind your clients of the way you contacted them. They'll remember that it was a pleasant experience, or they wouldn't have become clients in the first place. Use this reframe as a preemptive move by reviewing it before you ask for referrals.
Here's how you might use it:
You: Don, of all the things we've done so far, what's been the most valuable?
Don: Several things, actually. But if I had to mention one, you've helped me gain clarity about my financial future. I feel much more confident that I can accomplish my goals.
You: Great, I'm glad you're seeing the value in this work. Clarity is extremely important. I'm hoping we can brainstorm for a minute about others who might benefit from my work. Before you answer, let me explain how I'd contact them.

Actually, I'd contact them in much the same way I contacted you. I'd send a brief note to let them know I'll be calling - mentioning your name, of course. I'd follow up with a quick phone call to determine whether I might bring value to their situation. I'd never do anything to hurt your relationship with them or my relationship with you. With that in mind, could we brainstorm about this for a few minutes?
A COMFORTABLE APPROACH
Crafting an approach together is another reframing technique that will make everyone more comfortable. You might say, "Together, we could craft a way for you to introduce me - a way that will feel comfortable for everyone. Could we brainstorm about others you know who might benefit from my work?"
Most referral reluctance is a fear or concern your clients have about giving referrals. Explore their concern carefully, then reframe their thinking. If you don't address their core concern, you'll likely get nowhere with hesitant clients.