Why do some ions form tetrahedral complexes more readily than others?
Ligands use lone pairs of electrons to form coordinate bonds with the metal ion of the complex. The coordination number is the number of coordinate bonds from the ligands to the central ion. For instance, if a central ion has two coordinate bonds formed to it, one from each ligand, then the coordination number would be 2.(1)

According to Lumen Learning, for certain metals the maximum coordination number is related to the "electronic configuration of the metal ion (specifically, the number of empty orbitals) and to the ratio of the size of the ligands and the metal ion". Furthermore, it states that large metals with small ligands result in high coordination numbers, presumably due to there being more attraction from the positively charged central ion. Conversely, small metals with large ligands will have low coordination numbers, due to there being less electrostatic attraction towards the lone pairs on the ligands as its surface area is smaller.(2) Extrapolating this knowledge towards your question, we can parse the question to look at its components:

Co2+ is has an ionic radius of 74 pm while Fe2+ has an ionic radius of 76 pm. If we examine the example complex you gave, [CoCl4]2-, Chlorine has a large atomic radius of 175 pm relative to Co2+ ionic radius.(3) Using what we learned from Lumen Learning, this is a small central ion with relatively large ligands. Hence, the coordinate number must be smaller, such that it is 4, meaning it forms a complex with a tetrahedral geometry. Fe2+ on the other hand has an ionic radius of 76 pm and for a complex with an octahedral geometry, let us say [Fe(H2O)6]2+, it has 6 water molecules that function as ligands. The hydrogen and oxygen atoms have atomic radii of 25 and 60 pm respectively.(4) Consequently, the size of the water atoms are considerably smaller than the Chlorine atoms and thus, according to Lumen Learning, since we have smaller ligands, more of them can form coordinate bonds with the Fe2+ central ion. If we are to look at a different example, e.g. [Fe(CO)4]2−, we can see that it has ligands with large atomic radii (i.e. Carbon and Oxygen) and thus fewer ligands can bond with the central ion, resulting in a tetrahedral geometry.

References:


Brown, Catrin. "Chapter 3 – Periodicity." Higher Level Chemistry. Ed. Mike Ford. 2nd ed. N.p.: n.p., n.d. 123-33. Print.
Mott, Vallerie. "Introduction to Chemistry." Lumen. N.p., n.d. Web. 16 Apr. 2019.
"Cobalt Chemistry." Cobalt Transition Metal Chemistry Cobalt(II)Co2+ Complex Ions Stabilised Ligand Substitution Cobalt(III) Co3+ Complexes Redox Chemical Reactions +2 +3 Principal Oxidation States GCE AS A2 IB A Level Inorganic Chemistry Revision Notes. N.p., n.d. Web. 16 Apr. 2019.
Kwilkis. "Helium Atom, Radon Atom and Water Molecule Sizes and Concrete?" Helium Atom, Radon Atom and Water Molecule Size... | ACS Network. N.p., 03 Oct. 2018. Web. 16 Apr. 2019.