Parameter estimation in two-dimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics of ion channels. One such model is the stochastic Morris-Lecar model, where random fluctuations in conductance and synaptic input are specifically accounted for by the diffusion terms. It is defined through a non-linear two-dimensional stochastic differential equation with state dependent noise on the non-observed coordinate. The coordinates are coupled, i.e. the unobserved coordinate is non-autonomous, and we are therefore not in the more well-behaved situation of a hidden Markov model. In this paper, we propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation-Maximization algorithm. The performance is evaluated in a simulation study, and it turns out that even the rate scaling parameter governing the opening and closing of ion channels of the unobserved coordinate can be reasonably estimated. Also an experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed.