The best open source alternative to Timely is Dudle, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 50 alternatives to Timely and three of them is open source so hopefully you can find a suitable replacement. Other interesting open source alternatives to Timely are Booking Commerce (Freemium, Open Source) and Booking.js (Free, Open Source).
Booking Commerce is SaaS-based Online booking and Appointment Scheduling software that ease your customer onboarding process and get your sales rolling. Now you can power your business using world's first online comprehensive platform for bookings.