All of the tensor's components should have the same dimension. Notice, for example, that it doesn't make sense to speak of a vector with two entries having a dimension and another entry having another dimension. A similar principle holds for tensors.

From your matrix, the problem seems to be simply that you're writing $\Delta t$ when you really should be writing $c \Delta t$.

I find it somewhat complicated to define the stress-energy tensor in terms of its interpretation. It is cleaner to define it mathematically (for example, using the expressions on Wikipedia) and interpret it later. This will clear the difficulties with the manipulation of $c$'s and make it clear which entries in your tensor should be divided or multiplied by $c$.

The weird dimensions in your tensor seem to come from working with the coordinate $\lbrace t,x,y,z\rbrace$, which have different dimensions. Usually one works with $\lbrace ct,x,y,z\rbrace$, in which all of the components have the same dimensions. (Remark: the original version of this answer claimed all components of a tensor should have the same dimension but, as mike stone pointed out in the comments, this only holds if the coordinates all have the same dimension).

Hence, from your matrix, the problem seems to be simply that you're writing $\Delta t$ when you really should be writing $c \Delta t$.

I find it somewhat complicated to define the stress-energy tensor in terms of its interpretation. It is cleaner to define it mathematically (for example, using the expressions on Wikipedia) and interpret it later. This will clear the difficulties with the manipulation of $c$'s and make it clear which entries in your tensor should be divided or multiplied by $c$.