Rescuing old beginner's telescopes that are missing parts is only rarely cost effective. The basic problem is that by the time you buy the accessories needed to complete the telescope, you have spent as much money as what it would take to buy a new telescope, complete with all the accessories and, often, that money will get you a bigger and/or better model in a new model.
Let's see how this works. To do astronomy, you can get by with two eyepieces and a barlow and, yes, you should definitely add a diagonal. The price for two basic, but usable quality eyepiece will be about $30 each. Figure a bit more for a decent 2x barlow, maybe $40. A diagonal? Add another $40. You're already at $140 for a scope that was not much more than $50 brand new. Yes, you could probably shave that price down a bit by shopping for ultra cheap eyepieces, similar to what was originally supplied with the scope, but the cheap eyepieces supplied with beginner telescopes are, in a word, horrid. It's the first telescope accessory I recommend to replace to get the most out of a beginner's telescope.
If you decide to proceed with fixing up that old 60mm refractor, though, you should first measure the opening at the back of the focuser. A lot of these older scopes used obsolete .965" (1") accessories that are now almost non-existent. Whatbyou want is an opening of 1.25"
If you're going to spend $140, a better choice would be to jump up to a larger refractor, such as the Celestron Powerseeker 80 EQ with motor drive for $120. That extra size will definitely allow you to see more in the night sky and the motor drive gets you automatic tracking. Another great buy is the even larger 5" (127mm) Bushnell Ares Dobsonian
reflector for only $150.
Let us know what you decide to do. Appreciate the question.