Check out Krippendorff's alpha. It has several advantages over some other measures such as Cohen's Kappa, Fleiss's Kappa, Cronbach's alpha: it is robust to missing data (which I gather is the main concern you have); it is capable of dealing with more than 2 raters; and it can handle different types of scales: ( nominal, ordinal, etc. It), and it also accounts for chance agreements better than some other measures like Cohen's Kappa.
Calculation of Krippendorff's alpha is supported by several statistical software packages, including R (by the irr package), SPSS, etc.
Below are some relevant papers, that discuss Krippendorff's alpha including its properties and its implementation, and compare it with other measures:
Hayes, A. F., & Krippendorff, K. (2007). Answering the call for a standard reliability measure for coding data. Communication Methods and Measures, 1(1), 77-89.
Krippendorff, K. (2004). Reliability in Content Analysis: Some Common Misconceptions and Recommendations. Human Communication Research, 30(3), 411-433. doi: 10.1111/j.1468-2958.2004.tb00738.x
Chapter 3 in Krippendorff, K. (2013). Content Analysis: An Introduction to Its Methodology (3rd ed.): Sage.
There are some additional technical papers in Krippendorff's website